%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: s827.dvi %%Pages: 37 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMSY8 CMBX9 CMR9 CMMI9 CMSY9 MSBM10 CMMI6 %%+ CMBX12 CMR10 CMMI10 CMBX10 CMTI10 CMSY10 CMSY6 CMR8 CMR7 CMMI7 CMR6 %%+ CMMI8 CMSY7 CMEX10 CMSY5 CMMI5 CMR5 MSBM7 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o s827.ps s827.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2007.08.06:1126 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: psfrag.pro %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2CB7C8461B10646CD63AFEB7608468CA0FCFC4D3458FB43D22879B515 27DD9CCF44C2BFCD95A4DE911E4915FBC02335E9999FD9B546134081D6DA3792 EC4A76DEBA77635BE52E09986268A919CB48B5EFB1A1301EE0683CB5709BC8CE D819D799020CBA673BA39C911075501395B1FD20EAD392C9D5A8C9FD1198C737 D1A614CF0C0432F29DDEB4BF9DB026908DBE89EE522B7D55DE9BF64AFBE6248E 2E10466655EB9083E7D23E3F0EE26154F191BEBC9987930CD4B4CABE1275BDF9 8755EF3D531FDF91D54954FC53F15A38D1E8F8D1E36447484FA2C09D34813615 838B6330FEAE536D08376E4A0FDDF58CDF5647C9F1FF3A7D1ACAD376DB3CADB6 9459F7A5D4F1864863B79E9F93A1EDE8B99C3138D26227C01F6FE0AAC800F2E5 94DD81CF7B1355B642CE45CB532FC5B535D66EDFFEA076C009E87406D9772D71 848C3C53B7496A5D6B58679EF11E114C5F457C6A0D3CDE50278E4A89D5393B1C F877CF4E2142A4D045C4AA9138105D748903BACC28FD43DFEDB341E1FCDBE2EA D412498FBB5374D6836CFBEB13D4C2B7B9625C25B037FDA9DCC42F5679C4B3C1 6340E341F73A921013790936801297855EDE27C68907C6C87633FE64CBDCFEC9 DD8EC8784857A09FE395D7FE095A87CC113B930AD09643AC6F9F5A44A1154C89 7951C1CEF380FE489886299A1C5A2E1FB2D475FD3478BEDD0EC21A4CBAD46924 9AF698FCD47B9891629762AAD9E00C0C31B4F54AA5E59A575DB50A8961F05D7B D54237D5CE59FDB5C3E83AFEB532CC4F900F7E85358A528D56A6FBE9F3002E56 EA59E9C2459EEA543F906E74846306E52E324E00D300A78B984ADD86E21B5C08 4E19F5F28704CCA9BC6F5B8E11C74674881613A81A1763E4217B4FC14BD6FF18 B37A14375DF5F7CCD561DC7ABC388F4539424239C618F1D92CD37F507FF94133 927748C386DF1C1EA2F61DC341C76A4E72E64AA9723292B83079A9C3FCEA7355 51666A804736DB26A32A5E44562BF0EEC98870D116148D9E17AFD856254CF45F 25F15F274CD668C048FCC6AD42D003519C706E093B91CD448AE1F879F789D869 B1907F0AE617801BC19C7CBDBA68D819A0CC55652A2E737CAAF8B513CC95B593 004E2D4ACC07362FF705EC944AD11A89322C2B8F22640ACC07DE6247F524ED9B 54E6645A122774A70E1AC3B1CD4EF56DD526DCE88D27742285DE6A956F52AB83 885853C13481CEF4A9C518918D4ADFD9818E9B8F57BE56B5575FA1DA295DFB3B 1F528233265281FD7614B4CDE7D1D0DB66CDB1B7C1A53CEC9CB178CEA88005F0 3E482938AFFDB44E2C31E928F068B35EB7A91B910F2B2FBC769AA38806DC7FA1 973956477669BDE4702ABB9AFF6696247831A9D7212DE60A61A070E4D250F018 670F3354BEADAC44DC7F8CC4E56DF154BA250DAEB7F085FC417BD4F364BCC00B 2AA2E19F3F5B728DE0A42143EFAEA62DF1678A79D25D2E3D69CFEBA6C5844595 AE2D53DE40C091BEDF754155362627581E94EC9009DD04454CE9D9C53DE3F615 E4CB174176BC5479D9 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA06DA87FC7163A5A2A756A598FAB07633 89DE8BB201D5DB4627484A80A431B6AFDBBBF23D4157D4AFE17E6B1C853DD417 25F84CD55402AB88AB7EEFDEDBF2C2C731BD25567C53B474CCF739188A930039 098A197F9C4BE7594D79442B2C8A67447DE44698321145D7689B91EF235EA80E B600AA8E238064F154284096C4C2554EFE8DDF13AFF8D3CE30E0999375C0FEE6 F992DEA5FC3897E2CC8B7A90238E61E41622DE80F438DD994C73275CC52249D9 F6686F87F394FB7BB668138B210BEC9E46415A1B58C990B81E7D7DD301143517 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 80 /summationtext put dup 83 /uniontext put dup 88 /summationdisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 81 /Q put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D0037D33F24E2FAC2B0009AD3C8350CDF8CC 65BCA87979C36D14CB552E9A985E48BE4E88ECA16DF418749AF04FDD2B0E1380 D281BB2476BB45FF30946B247DFD7F57305FA87E50CA338121C71CDFDF927A9C 77FF14CB4A1D6D80356FB1171ED38C37702350497B44E42CE31DB2F493807DAA 15B887C671199A54C4C1294BC520F5538C15556BC43C9F62342B121C6DCD6C5F 491DA47FF360201EE21C08A781ED0589A6DF91B99FE118B9B29E4F068672E52F 1A06C514D91C4C937D4E642503392B1CD1B984B04B674C2977A634F63B35677E 9196FFCB03EE4215E3B3723395FAE498098182DC1BB96FFDAB0DCEA34121466F AF04749349EDADFE415A769772330B22DE1217A74D17D7E16E6164565F90B15A C1D43A9AB610214FDF53CC8A844931C6641FF2D24B054127DA44D99B3DDBE07C 7110FFA4550FD8960FC78275D9C43C1E4C61F862D4E9C51C37516DD7DF07E31B 4613759165F609E6473D689AD8D227FDB85CD3D8AB8B5E02B465D624710B96FD C1008F98B005FBB73CEFEE5A389BEF3464879A58CE59DB28E716A5F7B26CE804 4A9F2223A8D8852B3DABFBAD8E00C31225E9B6F01E81642165EE6C4A47DF2EAB 4FCB30A159B545800426EDC5D0ABC5C811F65A3180696D86516E979F6EB52220 05FD60A1142CD3B2F4F16EFD15EE9008B017C6201D5F1149758ABA2D0B5905FB 94A87F0C8387A1D3C7B40442B26C31BFDC658C7D4F8ABA63E81217348B37C02A A34C00C34A13C30DA212DAC5F25620FA78F1DFC043428A83A4F7B01583C71BAF CD64A063FAAB6918DD3AA0078B9A2BAC83A2B5FEB4769CE1A8E0372966B382EC 24BD2320FD60983220F554C7AA9A8924367C96C73A556CB17AA7BEF6DAAA7992 14DFB6CB870D34B0956ECBB3533C37714CD5F7ED40A74835FE241D845A2F988A 935B743036375285093B1C9F327FE4B6B598F09CF2BC73C7EA7EE06CCC6C8940 5CF01E8CE36991A9DBA1993718ED5E65A75732D84C4A75768E2028CBFDAAC3BA 34D6A304113587BFBE458C9BA056C02F94F311642D772B9B9121B7B54F9EFB6C 5E55E072B2E691117C54DB42CC7479EB1134F5D3BFA2DC6541C513313591055F C2DD5C1EEC432BAC 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F075EA0A10A15B0ED05D5039DA41B32B16E95 A3CE9725A429B35BAD796912FC328E3A28F96FCADA20A598E247755E7E7FF801 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Fr(W)37 b Fo(\022)25 b Fr(V)19 b Fs(\()1270 2772 y(\026)1248 2793 y Fr(H)7 b Fs(\),)30 b(where)e(w)n(e)g(only)h (coun)n(t)f(the)h(w)n(eigh)n(ts)-118 2893 y(of)d Fr(v)s Fs({)p Fr(W)37 b Fs(edges,)26 b(is)g(denoted)g(b)n(y)f(d)n(\026)-40 b(eg)1052 2913 y Fj(W)1128 2893 y Fs(\()p Fr(v)s Fs(\).)37 b(W)-7 b(e)26 b(shall)g(adopt)f(this)h(notation)g(for)f(our)-118 2993 y(w)n(eigh)n(ted)i(cluster)g(graph)753 2972 y(\026)731 2993 y Fr(H)7 b Fs(.)37 b(Similarly)-7 b(,)27 b(for)g(a)h(subset)f Fr(X)j Fo(\022)22 b Fr(V)1921 3005 y Fj(j)1957 2993 y Fs(,)27 b(w)n(e)h(write)844 3207 y(d)n(\026)-40 b(eg)969 3228 y Fj(X)1032 3207 y Fs(\()p Fr(V)1112 3219 y Fj(i)1141 3207 y Fs(\))23 b(:=)1317 3151 y Fr(e)p Fs(\()p Fr(X)r(;)14 b(V)1544 3163 y Fj(i)1571 3151 y Fs(\))p 1317 3188 287 4 v 1441 3264 a Fr(s)1614 3207 y(:)-118 3394 y Fs(F)-7 b(or)39 b(a)g(set)g Fo(Y)47 b Fs(of)39 b(subsets)g(of)h(distinct)g (clusters)e(from)h Fr(G)1776 3406 y Fj(p)1841 3394 y Fo(\000)26 b Fr(V)1980 3406 y Fj(i)2008 3394 y Fs(,)43 b(w)n(e)c(shall)g(write)-118 3494 y(d)n(\026)-40 b(eg)8 3514 y Fg(Y)61 3494 y Fs(\()p Fr(V)141 3506 y Fj(i)169 3494 y Fs(\))28 b(for)356 3432 y Fe(P)444 3519 y Fj(Y)14 b Fg(2Y)609 3494 y Fs(d)n(\026)-40 b(eg)735 3514 y Fj(Y)793 3494 y Fs(\()p Fr(V)873 3506 y Fj(i)901 3494 y Fs(\).)-118 3636 y(W)-7 b(e)31 b(shall)f(often)g(use)g(edges)g(of)927 3615 y(\026)905 3636 y Fr(H)38 b Fs(to)30 b(represen)n(t)f(the)i(resp)r (ectiv)n(e)e(subgraph)g(of)i Fr(G)2537 3648 y Fj(p)2575 3636 y Fs(,)-118 3735 y(or)26 b(its)h(v)n(ertex)f(set.)37 b(F)-7 b(or)26 b(example,)h(an)g(edge)f Fr(e)d Fs(=)g Fr(C)6 b(D)25 b Fo(2)e Fr(E)5 b Fs(\()1817 3714 y(\026)1795 3735 y Fr(H)i Fs(\),)28 b(migh)n(t)f(refer)f(to)h(the)-118 3835 y(subgraph)f(of)h Fr(G)401 3847 y Fj(p)468 3835 y Fs(induced)g(b)n(y)h Fr(C)c Fo([)18 b Fr(D)r Fs(,)28 b(or)e(to)i Fr(C)c Fo([)18 b Fr(D)30 b Fs(itself,)e(i.e.)f(in)h(d)n (\026)-40 b(eg)2208 3855 y Fj(e)2243 3835 y Fs(\()p Fr(V)2323 3847 y Fj(i)2352 3835 y Fs(\).)37 b(And)-118 3935 y(for)23 b(a)h(set)g Fr(U)32 b Fo(\022)23 b Fr(C)17 b Fo([)11 b Fr(D)r Fs(,)26 b(w)n(e)e(sometimes)f(use)h(the)h(shorthand)e Fr(e)11 b Fo(\\)g Fr(U)34 b Fs(for)23 b(\()p Fr(C)18 b Fo([)11 b Fr(D)r Fs(\))g Fo(\\)g Fr(U)e Fs(.)-118 4077 y(Let)37 b(us)g(review)f(some)g(basic)g(prop)r(erties)g(of)h Fr(G)1429 4089 y Fj(p)1505 4077 y Fs(and)1697 4056 y(\026)1676 4077 y Fr(H)6 b Fs(.)65 b(A)37 b(simple)g(calculation)-118 4176 y(sho)n(ws)26 b(that)i(for)f Fr(X)j Fo(2)23 b Fr(V)c Fs(\()725 4155 y(\026)703 4176 y Fr(H)7 b Fs(\))28 b(and)f(for)g Fo(Y)k(\022)22 b Fr(V)d Fs(\()1421 4155 y(\026)1399 4176 y Fr(H)7 b Fs(\))28 b(with)g Fr(X)39 b(=)-51 b Fo(2)23 b(Y)35 b Fs(w)n(e)27 b(ha)n(v)n(e)g(that)-18 4440 y(deg)107 4460 y Fg(Y)161 4440 y Fs(\()p Fr(v)s Fs(\))d Fr(>)e Fs(d)n(\026)-40 b(eg)505 4460 y Fg(Y)558 4440 y Fs(\()p Fr(X)7 b Fs(\))19 b Fo(\000)f Fr(")p Fo(jY)7 b(j)p Fr(s)27 b Fs(for)h(all)f(but)h(at)g(most)f Fr(\013s)h Fs(v)n(ertices)e Fr(v)31 b Fs(of)d Fr(X)r(;)99 b Fs(\(2\))-118 4603 y(and)33 b(if)h Fo(Y)193 4573 y Fg(0)250 4603 y Fs(is)f(a)g(set)g(of)g(subsets)g (of)g(the)h(clusters)f(in)g Fo(Y)7 b Fs(,)35 b(eac)n(h)e(of)g(size)g (at)g(least)g Fr(\013s)p Fs(,)-118 4703 y(then)-62 4867 y(deg)64 4887 y Fg(Y)113 4870 y Fd(0)140 4867 y Fs(\()p Fr(v)s Fs(\))24 b Fr(>)e Fs(d)n(\026)-40 b(e)q(g)484 4887 y Fg(Y)533 4870 y Fd(0)560 4867 y Fs(\()p Fr(X)7 b Fs(\))18 b Fo(\000)g Fs(2)p Fr(")p Fo(jY)7 b(j)p Fr(s)28 b Fs(for)f(all)g(but)h(at)g(most)f Fr(\013s)h Fs(v)n(ertices)f Fr(v)k Fs(of)c Fr(X)r(:)56 b Fs(\(3\))1219 5103 y(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop -118 1069 a Fs(These)29 b(v)n(ertices)g Fr(v)k Fs(will)d(b)r(e)g(called)f Fp(typic)l(al)k(with)f(r)l(esp)l(e)l (ct)g(to)e Fo(Y)7 b Fs(,)30 b(or)f(w.r.t.)h Fo(Y)2336 1039 y Fg(0)2359 1069 y Fs(.)44 b(If)30 b(no)-118 1168 y(confusion)d(is)h(p)r(ossible,)f(w)n(e)g(call)g Fr(v)k Fs(simply)d Fp(typic)l(al)p Fs(.)-118 1401 y Ff(2.2)112 b(The)38 b(matc)m(hing)-118 1554 y Fs(The)27 b(main)g(in)n(terest)g(in) g(this)g(subsection)g(is)g(Lemma)g(7,)g(whic)n(h)g(will)g(giv)n(e)f(us) h(imp)r(or-)-118 1654 y(tan)n(t)f(structural)g(information)g(on)g(the)h (cluster)f(graph)f Fr(H)33 b Fs(that)27 b(corresp)r(onds)e(to)h(the) -118 1753 y(graph)f Fr(G)i Fs(from)g(Theorem)e(2)i(\(or)f(Theorem)f (4\).)37 b(A)27 b(w)n(eak)n(er)d(v)-5 b(arian)n(t)26 b(of)h(this)g(lemma,)-118 1853 y(Lemma)g(8)g(b)r(elo)n(w,)h(app)r (eared)e(in)i([1].)-118 2002 y(F)-7 b(or)42 b(the)h(pro)r(of)f(of)h (Lemma)f(7,)47 b(w)n(e)42 b(need)h(a)f(simpli\014ed)h(v)n(ersion)f(of)g (the)h(Gallai-)-118 2102 y(Edmonds)36 b(matc)n(hing)g(theorem,)i(a)f (pro)r(of)f(of)g(whic)n(h)h(can)f(b)r(e)h(found)g(for)f(example)-118 2202 y(in)28 b([4)o(].)-118 2301 y(A)j(1-)p Fp(factor)p Fs(,)i(or)d Fp(p)l(erfe)l(ct)k(matching)p Fs(,)f(of)e(a)g(graph)f Fr(G)i Fs(is)f(a)g(1-regular)d(spanning)j(sub-)-118 2401 y(graph)26 b(of)h Fr(G)p Fs(.)37 b(W)-7 b(e)28 b(call)f Fr(G)g Fs(1)p Fp(-factor-critic)l(al)p Fs(,)i(if)f(for)f(eac)n(h)f Fr(v)g Fo(2)e Fr(V)19 b Fs(\()p Fr(G)p Fs(\),)28 b(there)f(exists)g(a) -118 2500 y(p)r(erfect)h(matc)n(hing)f(of)g Fr(G)19 b Fo(\000)f Fr(v)s Fs(.)-118 2667 y Fq(Theorem)25 b(6)g(\(Gallai,)g (Edmonds\).)35 b Fp(Every)25 b(gr)l(aph)h Fr(G)f Fp(c)l(ontains)f(a)h (set)f Fr(S)k Fo(\022)23 b Fr(V)c Fs(\()p Fr(G)p Fs(\))-118 2766 y Fp(so)31 b(that)f(e)l(ach)h(c)l(omp)l(onent)g(of)g Fr(G)19 b Fo(\000)g Fr(S)35 b Fp(is)30 b Fs(1)p Fp(-factor-critic)l (al,)j(and)e(so)f(that)h(ther)l(e)f(is)h(a)-118 2866 y(matching)d(in)f Fr(G)h Fp(that)f(matches)h(the)f(vertic)l(es)h(of)g Fr(S)k Fp(to)c(vertic)l(es)f(of)h(di\013er)l(ent)g(c)l(omp)l(o-)-118 2965 y(nents)h(of)h Fr(G)19 b Fo(\000)f Fr(S)5 b Fp(.)-118 3131 y Fs(W)-7 b(e)28 b(are)e(no)n(w)h(ready)g(for)g(one)g(of)h(the)g (k)n(ey)f(to)r(ols)g(in)h(the)g(pro)r(of)f(of)g(Theorem)g(2.)-118 3297 y Fq(Lemma)g(7.)37 b Fp(L)l(et)489 3277 y Fs(\026)468 3297 y Fr(H)32 b Fp(b)l(e)26 b(a)h(weighte)l(d)g(gr)l(aph)g(on)f Fr(N)35 b Fp(vertic)l(es,)28 b(and)e(let)g Fr(K)j Fo(2)23 b Fn(Q)p Fp(.)37 b(L)l(et)26 b Fr(L)-118 3397 y Fp(b)l(e)31 b(the)g(set)f(of)i(those)f(vertic)l(es)h Fr(v)c Fo(2)d Fr(V)19 b Fs(\()1139 3376 y(\026)1117 3397 y Fr(H)7 b Fs(\))31 b Fp(with)h Fs(d)n(\026)-40 b(eg)q(\()p Fr(v)s Fs(\))25 b Fo(\025)g Fr(K)6 b Fp(.)42 b(If)31 b Fo(j)p Fr(L)p Fo(j)25 b Fr(>)f(N)r(=)p Fs(2)p Fp(,)31 b(then)-118 3497 y(ther)l(e)26 b(ar)l(e)h(two)g(adjac)l(ent)g(vertic)l(es)g Fr(A;)14 b(B)28 b Fo(2)23 b Fr(L)p Fp(,)k(and)g(a)g(matching)g Fr(M)35 b Fp(in)2192 3476 y Fs(\026)2171 3497 y Fr(H)e Fp(such)26 b(that)-118 3596 y(one)k(of)g(the)g(fol)t(lowing)j(holds.) -122 3762 y(\(a\))41 b Fr(M)e Fp(c)l(overs)30 b Fr(N)9 b Fs(\()p Fr(A)19 b Fo([)g Fr(B)t Fs(\))p Fp(,)-118 3928 y(\(b\))41 b Fr(M)j Fp(c)l(overs)35 b Fr(N)9 b Fs(\()p Fr(A)p Fs(\))p Fp(,)38 b(and)d Fs(d)n(\026)-40 b(eg)967 3949 y Fj(L)p Fg([)p Fj(M)1131 3928 y Fs(\()p Fr(B)t Fs(\))33 b Fo(\025)f Fr(K)q(=)p Fs(2)p Fp(.)52 b(Mor)l(e)l(over,)38 b(e)l(ach)e(e)l(dge)g(in)f Fr(M)29 4028 y Fp(has)c(at)f(most)f(one)h (endvertex)g(in)g Fr(N)9 b Fs(\()p Fr(A)p Fs(\))p Fp(.)-118 4194 y(Pr)l(o)l(of.)43 b Fs(Observ)n(e)26 b(that)i(w)n(e)f(ma)n(y)g (assume)g(that)h Fr(Y)41 b Fs(:=)23 b Fr(V)c Fs(\()1731 4173 y(\026)1709 4194 y Fr(H)7 b Fs(\))19 b Fo(\000)f Fr(L)27 b Fs(is)g(indep)r(enden)n(t.)-118 4294 y(No)n(w,)32 b(Theorem)f(6)g(applied)g(to)g(the)h(un)n(w)n(eigh)n(ted)f(v)n(ersion)f (of)1919 4273 y(\026)1897 4294 y Fr(H)39 b Fs(yields)31 b(a)g(set)h Fr(S)i Fo(\022)-118 4393 y Fr(V)19 b Fs(\()3 4372 y(\026)-19 4393 y Fr(H)7 b Fs(\))39 b(and)h(a)e(matc)n(hing)h Fr(M)846 4363 y Fg(0)869 4393 y Fs(.)72 b(Fix)39 b Fr(S)44 b Fs(and)c(c)n(ho)r(ose)e Fr(M)1758 4363 y Fg(0)1820 4393 y Fs(so)g(that)i(it)g(con)n(tains)e(a)-118 4493 y(maximal)32 b(n)n(um)n(b)r(er)h(of)f(v)n(ertices)g(of)h Fr(Y)18 b Fs(.)53 b(Let)33 b Fr(M)41 b Fs(consist)32 b(of)h(the)g(union)g(of)g Fr(M)2409 4463 y Fg(0)2465 4493 y Fs(and)-118 4593 y(some)27 b(maximal)g(matc)n(hing)g(of)907 4572 y(\026)886 4593 y Fr(H)e Fo(\000)18 b Fr(V)h Fs(\()p Fr(M)1252 4563 y Fg(0)1275 4593 y Fs(\).)-118 4692 y(Set)27 b Fr(L)81 4662 y Fg(0)126 4692 y Fs(:=)c Fr(L)16 b Fo(n)f Fr(S)5 b Fs(.)36 b(Clearly)-7 b(,)26 b(if)h(there)f(is)g(an)g(edge)g Fr(AB)31 b Fs(with)26 b(endv)n(ertices)g Fr(A;)14 b(B)27 b Fo(2)d Fr(L)2553 4662 y Fg(0)2575 4692 y Fs(,)-118 4792 y(then)k(\(a\))g(holds.)36 b(Therefore,)27 b(w)n(e)g(ma)n(y)g (assume)g(that)h Fr(L)1680 4762 y Fg(0)1730 4792 y Fs(is)g(indep)r (enden)n(t.)1219 5103 y(7)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 561 1815 a /PSfrag where{pop(L')[[0()1 0]](L'')[[1()1 0]](S)[[2()1 0]](X)[[3()1 0]](Y)[[4()1 0]](S')[[5()1 0]](M)[[6()1 0]]7 0 -1/Begin PSfrag}{userdict /PSfrag{pop}put}ifelse 561 1815 a @beginspecial 0 @llx 0 @lly 257 @urx 160 @ury 1629 @rwi @setspecial %%BeginDocument: match.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: match.eps %%Creator: fig2dev Version 3.2 Patchlevel 5-alpha5 %%CreationDate: Tue Mar 13 17:52:56 2007 %%For: maya@kama (Maya Stein) %%BoundingBox: 0 0 257 160 %Magnification: 1.0000 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def /col32 {0.000 0.000 0.000 srgb} bind def end save newpath 0 160 moveto 0 0 lineto 257 0 lineto 257 160 lineto closepath clip newpath -33.3 187.8 translate 1 -1 scale % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index oldshow % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proc char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % right45 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 20 20 true [ 20 0 0 -20 0 20 ] {<0040100080200100400200800401000802001004 0020080040100080200000401000802001004002 0080040100080200100400200800401000802000>} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P5 exch def /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0 slj 0 slc 0.06299 0.06299 sc % % Fig objects follow % % % here starts figure with depth 50 % Polyline 0 slj 0 slc 15.000 slw n 2970 1530 m 3960 1530 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 198.00 102.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 1530 990 m 2520 990 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 102.00 66.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 1530 1350 m 2520 1350 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 102.00 90.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 1530 1710 m 2520 1710 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 102.00 114.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline 7.500 slw n 645 720 m 540 720 540 2865 105 arcto 4 {pop} repeat 540 2970 1785 2970 105 arcto 4 {pop} repeat 1890 2970 1890 825 105 arcto 4 {pop} repeat 1890 720 645 720 105 arcto 4 {pop} repeat cp gs col0 s gr % Polyline n 2265 720 m 2160 720 2160 2865 105 arcto 4 {pop} repeat 2160 2970 3225 2970 105 arcto 4 {pop} repeat 3330 2970 3330 825 105 arcto 4 {pop} repeat 3330 720 2265 720 105 arcto 4 {pop} repeat cp gs col0 s gr % Polyline n 3705 720 m 3600 720 3600 2865 105 arcto 4 {pop} repeat 3600 2970 4485 2970 105 arcto 4 {pop} repeat 4590 2970 4590 825 105 arcto 4 {pop} repeat 4590 720 3705 720 105 arcto 4 {pop} repeat cp gs col0 s gr % Polyline n 1260 2970 m 1260 720 l gs col0 s gr % Polyline n 4226 720 m 4234 720 l gs col0 s gr % Polyline n 4226 720 m 4234 720 l gs col0 s gr % Polyline n 4226 720 m 4234 720 l gs col0 s gr % Polyline n 4226 720 m 4234 720 l gs col0 s gr % Polyline n 4230 2970 m 4230 720 l gs col0 s gr % Polyline n 2160 1890 m 3330 1890 l gs col0 s gr % Polyline 15.000 slw n 2970 1080 m 3960 1080 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 198.00 72.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 2970 2160 m 3960 2160 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 198.00 144.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 1530 2520 m 2520 2520 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 102.00 168.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 1530 2160 m 2520 2160 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 102.00 144.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 2970 2610 m 3960 2610 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 198.00 174.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline 7.500 slw n 2745 1890 m 2745 2970 l gs col0 s gr /Times-Roman ff 190.50 scf sf 2700 630 m gs 1 -1 sc (S) col0 sh gr /Times-Roman ff 190.50 scf sf 2700 1350 m gs 1 -1 sc (L'') col0 sh gr /Times-Roman ff 190.50 scf sf 4365 1890 m gs 1 -1 sc (X) col0 sh gr /Times-Roman ff 190.50 scf sf 2295 2790 m gs 1 -1 sc (S') col0 sh gr /Times-Roman ff 190.50 scf sf 990 630 m gs 1 -1 sc (L') col0 sh gr /Times-Roman ff 190.50 scf sf 3960 630 m gs 1 -1 sc (Y) col0 sh gr /Times-Roman ff 190.50 scf sf 1440 2025 m gs 1 -1 sc ( M) col0 sh gr % here ends figure; $F2psEnd rs end showpage %%Trailer %EOF %%EndDocument @endspecial 561 1815 a /End PSfrag 561 1815 a 561 1027 a /Hide PSfrag 561 1027 a -179 1085 a Fs(PSfrag)26 b(replacemen)n(ts)p -179 1114 741 4 v 561 1117 a /Unhide PSfrag 561 1117 a 385 1178 a { 385 1178 a 208 1198 a Fx(L)260 1167 y Fm(0)304 1198 y Fy(=)21 b Fx(L)c Fw(n)h Fx(S)385 1178 y } 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1069 a Fs(Since)23 b Fo(j)p Fr(L)p Fo(j)f Fr(>)317 1036 y Fj(N)p 317 1050 59 4 v 330 1097 a Fk(2)386 1069 y Fs(,)i(this)f(implies)g(that)g Fr(M)31 b Fs(con)n(tains)22 b(a)g(edge)g Fr(AB)28 b Fs(with)23 b(b)r(oth)g Fr(A;)14 b(B)27 b Fo(2)d Fr(L)p Fs(.)-118 1182 y(W)-7 b(e)30 b(ma)n(y)f(assume)h(that)g Fr(A)d Fo(2)g Fr(L)909 1152 y Fg(0)962 1182 y Fs(and)j Fr(B)h Fo(2)1312 1161 y Fs(~)1302 1182 y Fr(L)p Fs(.)44 b(By)30 b(\(4\))q(,)g Fr(B)k Fs(has)c(a)f(neigh)n(b)r(our)g Fr(D)j Fs(in)-118 1282 y Fr(X)7 b Fs(.)36 b(Hence,)26 b(the)h(matc)n(hing)f Fr(M)878 1252 y Fg(0)917 1282 y Fo([)16 b Fr(B)t(D)i Fo(n)d Fr(AB)31 b Fs(co)n(v)n(ers)24 b(more)i(v)n(ertices)f(of)h Fr(Y)45 b Fs(than)27 b Fr(M)2576 1252 y Fg(0)-118 1381 y Fs(do)r(es,)g(a)g(con)n(tradiction)g(to)g(the)h(c)n(hoice)f(of)g Fr(M)1342 1351 y Fg(0)1365 1381 y Fs(.)p 2538 1381 4 57 v 2542 1329 50 4 v 2542 1381 V 2591 1381 4 57 v -118 1543 a(Note)21 b(that)f(in)h(the)g(case)f Fr(K)28 b Fo(\025)23 b Fr(N)r(=)p 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y(is)d(the)h(actual)f(em)n(b)r(edding)h(pro)r(cedure,)g(whic)n(h)f (w)n(e)g(divide)h(in)n(to)f(the)h(t)n(w)n(o)f(cases)f(giv)n(en)-118 4086 y(b)n(y)27 b(Lemma)h(7,)f(and)g(treat)g(separately)f(in)i (Subsections)g(3.6)e(and)i(3.7.)-118 4315 y Ff(3.1)112 b(Ov)m(erview)-118 4468 y Fs(In)30 b(this)f(subsection,)h(w)n(e)f (shall)h(giv)n(e)e(an)h(outline)h(of)g(our)e(pro)r(of)h(of)h(Theorem)f (2.)42 b(All)-118 4568 y(details)28 b(can)f(b)r(e)h(found)g(in)h(the)f (subsequen)n(t)f(subsections.)37 b(The)28 b(o)n(v)n(erview)e(is)i(mean) n(t)-118 4668 y(to)c(help)g(in)g(understanding)g(the)g(general)f(ideas) g(w)n(e)h(shall)f(emplo)n(y)-7 b(,)24 b(but)h(ma)n(y)e(also)g(b)r(e) -118 4767 y(skipp)r(ed,)k(as)g(it)g(con)n(tains)g(no)f(necessary)g (information)g(needed)h(to)g(follo)n(w)g(the)g(pro)r(of)-118 4867 y(of)g(Theorem)g(2.)1219 5103 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop -118 1069 a Fs(In)31 b(order)e(to)i(facilitate)g 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Fr(T)1979 4651 y Fj(A)2050 4639 y Fo([)17 b Fr(T)2171 4651 y Fj(B)2228 4639 y Fs(,)27 b(one)g(after)-118 4738 y(the)d(other,)h(lev)n(elwise,)e(in)n(to)h Fr(M)866 4750 y Fj(A)931 4738 y Fo([)11 b Fr(M)1078 4750 y Fj(B)1136 4738 y Fs(.)35 b(The)24 b(order)f(of)h(this)g(em)n(b)r (edding)h(pro)r(cedure)-118 4838 y(will)j(b)r(e)g(suc)n(h)f(that)h(the) g(already)e(em)n(b)r(edded)i(part)f(of)h Fr(T)1683 4808 y Fg(\003)1748 4838 y Fs(is)f(alw)n(a)n(ys)f(connected.)1199 5103 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop -118 1069 a Fs(Moreo)n(v)n(er,)30 b(the)j(structure)e(of)h(our)f(decomp)r(osition)g(of)h Fr(T)1745 1039 y Fg(\003)1782 1069 y Fs(,)i(and)d(the)i(fact)f(that)g (w)n(e)-118 1168 y(em)n(b)r(ed)40 b(the)g(trees)f(from)h Fr(T)781 1180 y Fj(A)861 1168 y Fo([)27 b Fr(T)992 1180 y Fj(B)1088 1168 y Fs(in)41 b(the)f(matc)n(hing)f(edges,)j(ensures)d (that)h(the)-118 1268 y(predecessor)26 b(of)h(an)n(y)g(v)n(ertex)g Fr(r)f Fo(2)e Fr(S)5 b(D)1094 1238 y Fj(A)1166 1268 y Fo([)19 b 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2800 y(In)38 b(case)f(\(b\))i(of)f(Lemma)f(7,)j(it)f(is)e (not)h(p)r(ossible)g(to)g(partition)f(the)h(matc)n(hing)g Fr(M)-118 2899 y Fs(in)n(to)f Fr(M)141 2911 y Fj(A)232 2899 y Fs(and)g Fr(M)484 2911 y Fj(B)578 2899 y Fs(so)f(that)879 2837 y Fe(S)962 2899 y Fr(T)1011 2911 y Fj(A)1102 2899 y Fs(\014ts)h(in)n(to)g Fr(M)1509 2911 y Fj(A)1600 2899 y Fs(and)1771 2837 y Fe(S)1854 2899 y Fr(T)1903 2911 y Fj(B)1997 2899 y Fs(\014ts)h(in)n(to)f Fr(M)2405 2911 y Fj(B)2461 2899 y Fs(,)j(as)-118 2999 y(in)c(case)f(\(a\).)62 b(More)35 b(precisely)-7 b(,)37 b(for)e(an)n(y)h(partition)f(of)h Fr(M)44 b Fs(in)n(to)36 b Fr(M)2092 3011 y Fj(A)2182 2999 y Fs(and)f Fr(M)2432 3011 y Fj(B)2489 2999 y Fs(,)j(if)-118 3098 y(deg)8 3119 y Fj(M)71 3127 y Fc(A)122 3098 y Fs(\()p Fr(A)p Fs(\))28 b(allo)n(ws)d(for)i(the)g(em)n(b)r(edding)g(of)g(a)f (forest)g(with)h(v)n(ertex)f(set)h(of)g(size)f Fr(t)2448 3110 y Fj(A)2529 3098 y Fs(in)-118 3198 y Fr(M)-37 3210 y Fj(A)17 3198 y Fs(,)i(then)h(deg)384 3218 y Fj(M)447 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y(\026)1454 4294 y Fr(T)1503 4306 y Fj(B)1560 4294 y Fs(.)37 b(Assume)28 b(that)785 4457 y Fo(j)p Fr(V)19 b Fs(\()907 4378 y Fe([)1030 4436 y Fs(\026)1014 4457 y Fr(T)1063 4469 y Fj(A)1116 4457 y Fs(\))p Fo(j)24 b(\025)e(j)p Fr(V)d Fs(\()1404 4378 y Fe([)1527 4436 y Fs(\026)1511 4457 y Fr(T)1560 4469 y Fj(B)1616 4457 y Fs(\))p Fo(j)p Fr(;)-118 4630 y Fs(and)27 b(set)h Fr(T)234 4600 y Fg(0)279 4630 y Fs(:=)23 b(\()p Fr(T)471 4642 y Fj(A)543 4630 y Fo([)c Fr(T)666 4642 y Fj(B)723 4630 y Fs(\))g Fo(n)f Fs(\()882 4609 y(\026)866 4630 y Fr(T)915 4642 y Fj(A)987 4630 y Fo([)1077 4609 y Fs(\026)1061 4630 y Fr(T)1110 4642 y Fj(B)1166 4630 y Fs(\).)-118 4767 y(Our)36 b(plan)h(no)n(w)f(is) g(to)h(\014rst)f(em)n(b)r(ed)h(the)h(trees)e(from)g Fr(T)1720 4737 y Fg(0)1767 4767 y Fo([)25 b Fr(T)1896 4779 y Fj(B)1989 4767 y Fs(and)37 b(to)f(p)r(ostp)r(one)-118 4867 y(the)28 b(em)n(b)r(edding)g(of)540 4804 y Fe(S)639 4846 y Fs(\026)623 4867 y Fr(T)672 4879 y Fj(A)754 4867 y Fs(to)f(later.)38 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b(lies)f(in)h Fr(M)369 1778 y Fj(F)424 1766 y Fs(.)37 b(Therefore,)26 b(w)n(e)h(shall)g(`switc)n(h')h(this)g(forest)f(to)g Fr(T)2043 1778 y Fj(A)2097 1766 y Fs(.)-118 1866 y(Let)c(us)g(explain)f (what)h(w)n(e)f(mean)h(b)n(y)f Fp(switching)p Fs(.)37 b(F)-7 b(or)22 b(eac)n(h)g(tree)g Fr(t)h Fo(2)h Fr(T)2118 1878 y Fj(B)2183 1866 y Fo(n)2250 1845 y Fs(\026)2234 1866 y Fr(T)2283 1878 y Fj(B)2339 1866 y Fs(,)g(delete)-118 1965 y(all)29 b(v)n(ertices)e(from)i Fr(t)g Fs(that)g(are)f(adjacen)n (t)h(to)f Fr(S)5 b(D)1441 1935 y Fj(B)1527 1965 y Fs(in)29 b Fr(T)1686 1935 y Fg(\003)1753 1965 y Fs(and)f(add)h(them)h(to)f Fr(S)5 b(D)2522 1935 y Fj(A)2575 1965 y Fs(.)-118 2065 y(Put)27 b(the)h(comp)r(onen)n(ts)g(of)f(what)h(remains)e(of)i Fr(t)g Fs(in)n(to)f Fr(T)1626 2077 y Fj(A)1680 2065 y Fs(.)-118 2165 y(After)20 b(switc)n(hing)g(all)f(trees)h Fr(t)j Fo(2)g Fr(T)930 2177 y Fj(B)990 2165 y Fo(n)1051 2144 y Fs(\026)1035 2165 y Fr(T)1084 2177 y Fj(B)1140 2165 y Fs(,)f(denote)e(b)n(y)f Fr(T)1601 2177 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y(In)k(step)f Fr(i)d Fo(\025)g Fs(1,)j(let)h Fr(x)556 3059 y Fj(i)607 3047 y Fo(2)d Fr(V)19 b Fs(\()p Fr(T)846 3016 y Fg(\003)883 3047 y Fs(\))27 b(b)r(e)g(maximal)f(in)h (the)g(tree-order)e(of)h Fr(V)19 b Fs(\()p Fr(T)2266 3016 y Fj(i)p Fg(\000)p Fk(1)2378 3047 y Fs(\))27 b(with)880 3229 y Fo(j)p Fr(V)19 b Fs(\()p Fr(T)1063 3195 y Fj(i)p Fg(\000)p Fk(1)1175 3229 y Fs(\()p Fr(x)1254 3241 y Fj(i)1282 3229 y Fs(\)\))p Fo(j)24 b Fr(>)e(\014)t(k)s(;)892 b Fs(\(8\))-118 3412 y(and)27 b(de\014ne)704 3511 y Fr(T)765 3477 y Fj(i)815 3511 y Fs(:=)c Fr(T)987 3477 y Fj(i)p Fg(\000)p Fk(1)1117 3511 y Fo(\000)18 b Fs(\()p Fr(T)1293 3477 y Fj(i)p Fg(\000)p Fk(1)1405 3511 y Fs(\()p Fr(x)1484 3523 y Fj(i)1512 3511 y Fs(\))h Fo(\000)f Fr(x)1693 3523 y Fj(i)1721 3511 y Fs(\))p Fr(;)-118 3661 y Fs(as)32 b(illustrated)h(in)h(Figure)f(2\(a\).)53 b(If)34 b(there)f(is)g(no)g(v) n(ertex)f(satisfying)i(\(8\),)h(then)e(set)-118 3761 y Fr(x)-71 3773 y Fj(i)-20 3761 y Fs(:=)23 b Fr(R)q Fs(,)h(and)g(stop)f 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c4a19d7f679bee239adf1d1ce73e21352732f18c91ecd863cec1a8e2ae5d2430 43473b8cc8e24360b434fd796807f2261d6de0c5ebabe9b6c486e9efa35e0601 6e653d815b4c0129514ef9a05b216640044add5cb3da5ec3abcd7280b30e3327 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /F7 /FKHMFK+CMR7 [ /Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon /Phi/Psi/Omega/ff/fi/fl/ffi/ffl /dotlessi/dotlessj/grave/acute/caron/breve/macron/ring /cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash /suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash /zero/one/two/three/four/five/six/seven /eight/nine/colon/semicolon/exclamdown/equal/questiondown/question /at/A/B/C/D/E/F/G /H/I/J/K/L/M/N/O /P/Q/R/S/T/U/V/W /X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent /quoteleft/a/b/c/d/e/f/g /h/i/j/k/l/m/n/o /p/q/r/s/t/u/v/w /x/y/z/endash/emdash/hungarumlaut/tilde/dieresis /suppress/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma /Upsilon/Phi/Psi/.notdef/.notdef/Omega/ff/fi /fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron /breve/macron/ring/cedilla/germandbls/ae/oe/oslash /AE/OE/Oslash/suppress/dieresis/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef ] ipeMakeFont %%BeginResource: font RFAIEZ+CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /RFAIEZ+CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 2bdbf16fbc7512faa308a093fe5cf7158f1163bc1f3352e22a1452e73feca8a4 87100fb1ffc4c8af409b2067537220e605da0852ca49839e1386af9d7a1a455f 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4cf8e8410e0311297d1e1dceb8c8a662c6735da66e9cd443 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /F8 /RFAIEZ+CMR10 [ /Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon /Phi/Psi/Omega/ff/fi/fl/ffi/ffl /dotlessi/dotlessj/grave/acute/caron/breve/macron/ring /cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash /suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash /zero/one/two/three/four/five/six/seven /eight/nine/colon/semicolon/exclamdown/equal/questiondown/question /at/A/B/C/D/E/F/G /H/I/J/K/L/M/N/O /P/Q/R/S/T/U/V/W /X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent /quoteleft/a/b/c/d/e/f/g /h/i/j/k/l/m/n/o /p/q/r/s/t/u/v/w /x/y/z/endash/emdash/hungarumlaut/tilde/dieresis /suppress/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma /Upsilon/Phi/Psi/.notdef/.notdef/Omega/ff/fi /fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron /breve/macron/ring/cedilla/germandbls/ae/oe/oslash /AE/OE/Oslash/suppress/dieresis/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef ] ipeMakeFont %%BeginResource: font JJTZZA+CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /JJTZZA+CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 105 /i put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec d9d66f633b846a97b686a97e45a3d0aa0529731c99a784ccbe85b4993b2eebde 3b12d472b7cf54651ef21185116a69ab1096ed4bad2f646635e019b6417cc77b 532f85d811c70d1429a19a5307ef63eb5c5e02c89fc6c20f6d9d89e7d91fe470 b72befda23f5df76be05af4ce93137a219ed8a04a9d7d6fdf37e6b7fcde0d90b 986423e5960a5d9fbb4c956556e8df90cbfaec476fa36fd9a5c8175c9af513fe d919c2ddd26bdc0d99398b9f4d03d77639df1232a4d6233a9caf69b151dfd33f c0962eac6e3ebfb8ad256a3c654eaaf9a50c51bc6fa90b61b60401c235afab7b 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /F10 /JJTZZA+CMMI7 [ /Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon /Phi/Psi/Omega/alpha/beta/gamma/delta/epsilon1 /zeta/eta/theta/iota/kappa/lambda/mu/nu /xi/pi/rho/sigma/tau/upsilon/phi/chi /psi/omega/epsilon/theta1/pi1/rho1/sigma1/phi1 /arrowlefttophalf/arrowleftbothalf/arrowrighttophalf/arrowrightbothalf/arrowhookleft/arrowhookright/triangleright/triangleleft /zerooldstyle/oneoldstyle/twooldstyle/threeoldstyle/fouroldstyle/fiveoldstyle/sixoldstyle/sevenoldstyle /eightoldstyle/nineoldstyle/period/comma/less/slash/greater/star /partialdiff/A/B/C/D/E/F/G /H/I/J/K/L/M/N/O /P/Q/R/S/T/U/V/W /X/Y/Z/flat/natural/sharp/slurbelow/slurabove /lscript/a/b/c/d/e/f/g /h/i/j/k/l/m/n/o /p/q/r/s/t/u/v/w /x/y/z/dotlessi/dotlessj/weierstrass/vector/tie /psi/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma /Upsilon/Phi/Psi/.notdef/.notdef/Omega/alpha/beta /gamma/delta/epsilon1/zeta/eta/theta/iota/kappa /lambda/mu/nu/xi/pi/rho/sigma/tau /upsilon/phi/chi/psi/tie/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef ] ipeMakeFont %%BeginResource: font SXQXCN+CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /SXQXCN+CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 84 /T put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec d9d66f633b846a97b686a97e45a3d0aa0529731c99a784ccbe85b4993b2eebde 3b12d472b7cf54651ef21185116a69ab1096ed4bad2f646635e019b6417cc77b 532f85d811c70d1429a19a5307ef63eb5c5e02c89fc6c20f6d9d89e7d91fe470 b72befda23f5df76be05af4ce93137a219ed8a04a9d7d6fdf37e6b7fcde0d90b 986423e5960a5d9fbb4c956556e8df90cbfaec476fa36fd9a5c8175c9af513fe d919c2ddd26bdc0d99398b9f4d03d5993dfc0930297866e1cd0a319b6b1fd958 9e394a533a081c36d456a09920001a3d2199583eb9b84b4dee08e3d12939e321 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