Welcome to Professor Loebl's Discrete Mathematics Page
Exploring the beauty of discrete mathematics together.
I am affiliated with the Department of Applied Mathematics, Charles University, Prague.
Teaching
Vyucovane prednasky najdete na stránce katedry. Konzultace: dohoda e-mailem.
Diskretni a spojita optimalizace 2024
Diskretni a spojita optimalizace 2025
Discretni cast. Literatura: lecture notes and Cook, Cunningham, Pulleyblank, Schrijver, Combinatorial Optimisation, Wiley 1998.
Cviceni: Je nutne absolvovat diskretni i spojitou cast. Pro zapocet z diskretni casti je nutne jedno z nasledujicich: a. pisemny test nebo b. tymova prezentace zajimaveho tematu souvisejiciho s prednaskou, nebo c. tymova prezentace vypoctovych experimentu souvisejicich s prednaskou.
Unor 22: uvod, opakovani zakladnich pojmu teorie grafu, eulerovska prochazka, prostor cyklu grafu, Hamiltonovska kruznice, kostra grafu, rovinne grafy.
Unor 23 cviceni: opakovani zakladnich pojmu teorie grafu.
Unor 29: matroidy: zakladni definice, radova funkce, submodularita a jeji vyznam v modelovani utility.
Brezen 1 cviceni: basic notions of matroids, prove that vectorial and graphic "matroids" are indeed matroids. Prove that U(2,4) is not representable over F2.
Brezen 7: matroidy: hladovy algoritmus, dualni matroid, grafovy matroid
Brezen 8 cviceni: Let G be an embedded planar graph. Proof that the dual of its graphic matroid is isomorphic to the graphic matroid of its geometric dual.
skripta Matroidy1
skripta Matroidy2
skripta Matroidy3
Brezen 14: parovani v grafech, Tutte-Berge Theorem, Edmonds algorithm
skripta Parovani
Brezen 22: parovani a hranove rezy v rovinnych grafech, Isingova particni funkce
skripta Kasteleynova teorie
Brezen 29: Chinese postman problem a Problem obchodniho cestujiciho (TSP)
skripta czech Cinsky.postak.Obchodni.cestujici
skripta english Chinese.Postman.Travelling.Salesman
Exam topics (discrete part): (1) Matroids: basic examples and definitions (2) matroid rank function and submodularity (3) duality of matroids (4) greedy algorithm (5) Tutte theorem for matching (6) Chinese postman and Travelling salesman problems
Linearni Programovani 2024
Cviceni: pravidla na udeleni zapoctu stanovena cvicicimi.
23. unora: uvod, uloha linerniho programovani, priklady, opakovani linearni algebry
skripta Uvod_do_LP
skripta Prostor cyklu grafu
1. brezna: uloha linerniho programovani, standardni tvar, simplexova metoda
8. brezna: simplexova metoda, pivotovaci pravidla
15. brezna: pivotovaci pravidla, Blamdovo pravidlo
skripta Simplexova metoda
skripta Blandovo pravidlo
22. brezna: dualita
5. dubna: dualita, Fourier-Motzkinova eliminace
skripta Dualita LP
skripta FM eliminace, v. oddelovani
12. dubna: uloha diskretni optimalizace, Minkowski-Weylova veta; skripta dole do str. 6 vcetne
skripticka Diskretni optimalizace
19. dubna: uloha diskretni optimalizace; skripta do str. 12 vcetne
26. dubna: uloha diskretni optimalizace; skripta do konce
3. kvetna: primarni dualni algoritmy, vazene parovani v bipartitnich grafech, stabilni parovani
skripticka Primarni-dualni algoritmy
skripticka Stabilni parovani
10. kvetna: primarni dualni algoritmy, vazene parovani v obecnych grafech
skripticka Primarni-dualni algoritmy
17. kvetna: primarni dualni algoritmy dokonceni
zkusebni okruhy:
(1) Standardni tvar LP, vrchol, steny, bazicka reseni
(2) Simplexova metoda
(3) Pivotovaci pravidla geometricky
(4) Blandovo pravidlo
(5) Dualita: zneni, slaba a silna veta, podminky komplementarity
(6) Farkasovo lemma a dualita
(7) Dukaz vety o dualite
(8) Fourier-Motzkinova eliminace
(9) Veta o oddelovani
(10) Minkowski-Weylova veta
(11) Racionalni a celociselne mnohosteny
(12) TU matice a Hoffman-Kruskalova veta
(13) Chvatalovy rezy
(14) Primarni dualni algoritmy
Zaklady Nelinearni Optimalizece 2024
Zaklady Nelinearni Optimalizece 2024
Ucim druhou polovinu semestru Max Cut na plochach a Semidefinitni Programovani.
Uvod do problemu maximalniho rezu, maximalni rez na plochach, maximalni rez jako semidefinitni program.
10.12.: Semidefinitni programovani
17.12.: Lovaszova Theta funkce
5.1.: Lovaszova Theta funkce
skripta Nelinearni programovani
Diskretni a spojita optimalizace 2025
Discrete and Continuous Optimisation 2025
Discrete part. Literature: lecture notes and Cook, Cunningham, Pulleyblank, Schrijver, Combinatorial Optimisation, Wiley 1998.
Tutorials: It is necessary to pass both discrete and continuous part of the tutorial. For the discrete part, in order to pass you need one of the following: a. pass a test or b. make a team presentation of an interesting topic related to the lecture or c. make a team presentation of computer experiments related to topics of the lecture. I need to approve the teams and topics for b., c.
February 19: introduction, repetition of basic notions of the graph theory, euler tour, cycle space of a graph, Hamiltoniam cycles, Sperner trees, min spanning tree, planar graphs and their geometric duals.
February 26: matroids: basic definitions, rank function, submodularity and its significance for modelling utility
February 25 tutorial: basic notions of graph theory related to matroids
March 5: matroids: greedy algorithm, dual matroid, graphic matroid, independent and dependent set of a matroid
March 4 tutorial: Prove that vectorial and graphic "matroids" are indeed matroids. Prove that U(2,4) is not representable over F2.Let G be an embedded planar graph. Proof that the dual of its graphic matroid is isomorphic to the graphic matroid of its geometric dual.
skripta Matroidy1
skripta Matroidy2
skripta Matroidy3
March 12: matching in graphs, Tutte-Berge Theorem, Edmonds algorithm
skripta Parovani
March 19: matchings and edge-cuts in planar graphs, Ising partition function
skripta Kasteleynova teorie
March 26:Chinese postman and Travelling salesman problem
skripta czech Cinsky.postak.Obchodni.cestujici
skripta english Chinese.Postman.Travelling.Salesman
April 2: repetition
Exam topics (discrete part): (1) Matroids: basic examples and definitions (2) matroid rank function and submodularity (3) duality of matroids (4) greedy algorithm (5) Tutte theorem for matching (6) Chinese postman and Travelling salesman problems
Teorie her pro inteligentni site 2021
NOPT057 Teorie her pro inteligentní sítě 2021
ZOOM Meeting ID: 984 1389 7116 Passcode: 990697
Úterý 9.00
Webová stránka přednášky: https://kam.mff.cuni.cz/~cerny/teach/seminar.html
Linearni Algebra 2021
30.3.: Determinanty: úvod, příklady, základní pozorování, Gaussova eliminace
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_12.mp4
Lecture notes Determinanty
6.4.: Determinanty: Cramerovo pravidlo, aplikace determinantu
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_13.mp4
Lecture notes Determinanty
11.5.: Pozitivně definitní a pozitivně semidefinitní matice
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_14.mp4
Lecture notes Pozitivně (semi)definitní matice
18.5.: Pozitivně definitní a pozitivně semidefinitní matice
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_15.mp4
Lecture notes Pozitivně (semi)definitní matice
25.5.: Bilineární a kvadratické formy
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_16.mp4
Lecture notes Bilineární a kvadratické formy
1.6.: Bilineární a kvadratické formy
The video is available at https://kam.mff.cuni.cz/~loebl/video/zoom_17.mp4
Lecture notes Bilineární a kvadratické formy
Linearni Programovani 2020
Cviceni: pravidla na udeleni zapoctu stanovena cvicicimi.
18. unora: uvod, uloha linerniho programovani, priklady, opakovani linearni algebry
25. unora: standardni tvar ulohy LP, prevody na standardni tvar. Bazicke pripustne reseni
3. brezna: simplexova metoda, neomezenost, degenerace, jak najit pocatecni pripustna reseni, pivotovaci pravidla
skripticka Simplexova metoda
skripticka Blandovo pravidlo
10. brezna: pivotovaci pravidla, konecnost Blandova pravidla
17. brezna: dualita
24. brezna: dualita
skripticka Dualita LP
1. dubna: uloha diskretni optimalizace, Minkowski-Weylova veta; skripta dole do str. 4 vcetne
skripticka Diskretni optimalizace
8. dubna: uloha diskretni optimalizace; skripta do str. 8 vcetne
15. dubna: uloha diskretni optimalizace; skripta do str. 12 vcetne
22. dubna: uloha diskretni optimalizace; skripta do konce
29. dubna: opakovani cele diskretni optimalizace
29. dubna: pravidelne konzultace v 10.00. NAVIC konzultace v 18.00
6. kvetna: algoritmy primal-dual; skripta Primal Dual do str.5 vcetne
13. kvetna: algoritmy primal-dual; skripta Primal Dual do str. 8 vcetne
20. kvetna: algoritmy primal-dual; skripta Primal Dual cele; celkove opakovani; max parovani v obecnych grafech se nebude zkouset.
!!!! Zoom meeting: konzultace Martin Loebl (jmeno ale je Martin Mares)
Time: May 13, May 20, 2020 10:00
Join Zoom Meeting https://matfyz.zoom.us/j/93913950385
Meeting ID: 93913950385
Diskretni a spojita optimalizace 2018
Cviceni: pravidla na udeleni zapoctu stanovena cvicicim.
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21. unora: uvod, ulohy optimalizace, priklady
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28. unora: parovani
skripticka Parovani
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7. brezna: matroidy
skripticka Matroidy
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14. brezna: problem obchodniho cestujiciho
skripticka Problem obchodniho ceastujiciho
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21. brezna: optimalizace enumeracemi
skripticka Optimalizace enumeracemi
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28. brezna: kvantove pocitani
skripticka Kvantove pocitani
Témata diplomových prací
- Optimization in Sociology: Median of partitions. The aim is to study the problem to find a median of given set-partitions, with respect to a given distance. Such problems appear in Sociology and Biology, but it turns out that some natural graph theoretic and matroidal questions can be formulated in this language (1 student).
- Discrete Applied Mathematics: Theory of Kasteleyn orientations. This theory started in the 1960's by a seminal result of Kasteleyn about enumeration of perfect matchings of planar graphs. At present, this theory is applied in many diverse areas, e.g., statistical physics, graph colorings, algorithms and complexity, knot theory and spin networks, quantum computing (2 students).
- Bioinformatics: The role of repeats in DNA. DNA contains families of repeats, whose function is unclear. The aim is to study repeats with methods of graph theory, and also to do computer experiments towards understanding the repeats (1 student).
- Discrete Optimisation: Generation of random objects. The topic aims to include some global conditions in optimisation by combining optimisation and random generation methods, for practical problems.
- Graph Theory: Directed Cycle Double Covers. The aim is to study a well-known conjecture, if any 2-connected graph has a directed cycle double cover (2 students).
CV
Publications
Preprints
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M. Loebl, A. Jedlickova, J. Cerny Balancing Market Equilibria With Buying Rights (2025).
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M. Chudnovsky, M. Loebl, P. Seymour Small Families Under Subdivision arXiv:1910.04609 (2019).
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A. Jimenez, M. Loebl, Directed cycle double covers cut-obstacles and robust ear decompositions preprint 2018
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M. Kiwi, M. Loebl, Bijective proof of Kasteleyn's toroidal perfect matching cancellation theorem preprint 2018
Patents
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J. Blamey, L. Kencl, M. Loebl, Uprava informace v systému, patent Ceská Republika 2010.
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J. Blamey, L. Kencl, M. Loebl, Information concealing, patent U.S.A. 2015.
Books
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M. Klazar, J. Kratochvil, M. Loebl, R.Thomas, P. Valtr (eds) Topics in Discrete Mathematics: Dedicated to Jarik Nešetřil on the Occasion of his 60th birthday, ISBN 978-3-540-33700-3, Springer Verlag, Series Algorithms and Combinatorics (2006); received Prize of Rector of Charles University.
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M. Loebl, Discrete Mathematics in Statistical Physics, Vieweg+Teubner, Wiesbaden (2010) ISBN 978-3-834-89329-1(Print) 978-3-528-03219-7(Online).
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M. Loebl, J. Nesetril, R. Thomas (eds), A Journey Through Discrete Mathematics: A Tribute to Jiri Matousek, Springer Verlag (2017) ISBN 978-3-319-44479-6.
Publications
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D. Sychrovsky, J. Cerny, A. Jedlickova, M. Loebl Balancing Efficiency and Equity in Distribution Crises 5th International Workshop on autonomous Agents for Social Good (AASG) 2024, earlier version arXiv:2207.00898 (2022).
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D. Sychrovsky, S.Desai, M. Loebl Rule Enforsing Through Ordering 14th Conference on Decision and Game Theory for Security GameSec 2023, earlier version 14th Workshop on Optimization and Learning in Multiagent Systems OptLearnMAS 2023.
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D.Sychrovsky, J. Cerny, S. Lichau, M. Loebl Price of Anarchy in a Double-Sided Critical Goods Distribution System 22nd International Conference on Autonomous Agents and Multiagent Systems AAMAS 2023.
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J. Fink, M. Loebl, P. Pelikanova Arc-routing for winter road maintenance Discrete Optimization 41 (2021)
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M. Loebl, The Precise Complexity of Finding Rainbow Even Matchings Proceedings of the 8th International Conference on Algebraic Informatics, CAI 2019, LNCS 11545.
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M. Loebl, J.S. Sereni, Isomorphism of weighted trees and Stanley's conjecture for caterpillars Annales de l'Institute Henri Poincare D- European Mathematical Society 6,3 (2019)
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M. Loebl, Binary linear codes via 4D discrete Ihara-Selberg function Annales de l'Institute Henri Poincare D- European Mathematical Society 6,1 (2019)
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R. Aharoni, N. Alon, E. Berger, M. Chudnovsky, D. Kotlar, M. Loebl, R. Ziv Fair representation by independent sets in A Journey Through Discrete Mathematics: A Tribute to Jiri Matousek, Springer (2017).
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A. Jimenez, M. Kang, M. Loebl, Cubic bridgeless graphs and braces Graphs and Combinatorics 32-4 (2016).
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M. Loebl, P. Rytir, Binary linear codes, dimers and hypermatrices 10th Random Generation of Combinatorial Structures (GASCom) (2016);
also in: Electronic Notes in Discrete Mathematics 59 (2017), 19--35. -
R. Aharoni, M. Loebl, The Odd Case of Rota's Bases Conjecture Advances in Mathematics 282 (2015) 427-442
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M. Loebl, P. Somberg, Discrete Dirac Operators, Critical Embeddings and Ihara-Selberg Functions The Electronic Journal of Combinatorics 22, 1 (2015)
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A. Jimenez, M. Loebl, Directed cycle double cover conjecture: fork graphs ICGT 2014
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M. Klazar, M. Loebl, I. Moffatt, The Potts model and chromatic functions of graphs Annales de'l Institut Henri Poincare D (combinatorics, Physics and their Interactions) 1(1) 47- 60 (2014)
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I. Kriz, M. Loebl, P. Somberg, On Discrete Field Theory Properties of the Dimer and Ising Models and Their Conformal Field Theory Limits J. Math. Phys. 54, pp.053513-1--053513-25, (2013)
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M. Kang, A. Jimenez, M. Loebl, Directed Cycle Double Covers: Hexagon graphs Eurocomb 2013
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E, Berger, K. Choromanski, M. Chudnovsky, J. Fox, M. loebl, A. Scott, P. Seymour, S. Thomasse, Tournaments and colouring J.Comb.Theory, Ser.B 103(1) 1- 20 (2013)
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H. Teimoori-Faal, M. Loebl, Bass' identity and a coin arrangements lemma European Journal of Combinatorics 33,5 (2012).
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M. Loebl, G. Masbaum, On the optimality of the Arf invariant formula for graph polynomials Advances in Mathematics 226 (2011)
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M. Loebl, I. Moffatt, A permanent formula for the Jones polynomial Advances in Applied Mathematics 47,4 (2011).
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L. Kencl, M. Loebl, DNA-inspired information concealing: a survey Computer Science Review 4 (2010)
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M. Loebl, B. Reed, A. Scott, A. Thomason, S. Thomasse, Almost all H-free graphs have the Erdes-Hajnal property in: An irregular mind (Szemeredi is 70), Barany, Solymosi eds. Bolyai Society Mathematical Studies 41 (2010)
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Andrea Jimenez, Marcos Kiwi, Martin Loebl, Satisfying states of triangulations of a convex n-gon The Electronic J. of Combinatorics 17 (2010).
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M. Kang, M. loebl, The enumeration of planar graphs via Wick's theorem Advances in Mathematics 221 (5) 2009
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M. Kiwi, M. Loebl,Towards the Distribution of the Size of a Largest Planar Matching and Largest Planar Subgraph in Random Bipartite Graphs Electronic J. Combinatorics 15(1) 2008 R135
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M. Loebl, I. Moffatt,The chromatic polynomial of fatgraphs and its categorification Advances in Mathematics 217, 2008
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M. Loebl, Chromatic Polynomial, q-Binomial Counting and Colored Jones Function Advances in Mathematics 211-2, 2007
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M. loebl, Some discrete tools in statistical physics chapter in: Physics and Theoretical Computer Science, J.P. Gazeau, J. Nesetril, B. Rovan eds., IOS Press 2006
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M. Loebl, L. Zdeborova, The 3D Dimer and Ising Problems Revisited European J. Combinatorics 29/3, 2008
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S. Garoufalidis, M. Loebl,A non-commutative formula for the Colored Jones Function Math. Annalen 2006
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W. Krauth, M. Loebl,Jamming and Geometric Representations of Graphs Electronic J. Combinatorics R56, 2006
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R.A. Brualdi, M. Loebl, O. Pangrac,Perfect Matching Preservers Electronic J. Combinatorics R95, 2006
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S. Garoufalidis, M. Loebl,Random Walks and the Colored Jones Function Combinatorica 25/6 2005
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M. Janata, M. Loebl, Jacint Szabo,The Edmonds-Gallai Decomposition for the k-Piece Packing Problem Electronic Journal of Combinatorics 12, 2005
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M. Kiwi, M. Loebl, J. Matousek,Expected Length of the Longest Common Subsequence For Large Alphabets Advances in Mathematics 197 2005
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M. Loebl,Ground State Incongruence in Spin Glasses Revisited Electronic Journal of Combinatorics 11 (1) 2004
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M. Loebl, J. Matousek, O. Pangrac,Triangles in Random Graphs Discrete Mathematics 89 (1-3) 2004
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M. Loebl,A Discrete Non-Pfaffian Aproach to the Ising Problem DIMACS, Series in Discrete Mathematics and Theoretical Computer Science, Vol. 63, 2004
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M. Loebl, J. Vondrak, Towards a Theory of frustrated degeneracy Discrete Mathematics 271, 179-193, 2003.
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M. Loebl, J. Nesetril, B. Reed, A note on random homomorphisms from arbitrary graphs to Z Discrete Mathematics 273 (1-3) 2003
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M. Loebl, On the Dimer Problem and the Ising Problem in 3-dimensional Lattices Electronic Journal of Combinatorics R30 9(1), 2002
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M. Kiwi, M. Loebl, Largest Planar Matching in Random Bipartite Graphs Random Structures and Algorithms 21(2) 162-181, 2002
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A. Galluccio, M. Loebl, J. Vondrak, Optimization via Enumeration: a New Algorithm for the Max Cut Problem Mathematical Programming 90 (2001)2, 273-290
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M. Loebl, M. Matamala, Some Remarks on Cycles in Graphs and Digraphs Discrete Mathematics 233 (2001) 175-182
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A. Galluccio, M. Loebl, J. Vondrak, A New Algorithm for the Ising Problem: Partition Function for Finite Lattice Graphs
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A. Galluccio, M. Loebl, A Theory of Pfaffian Orientations I Electronic Journal of Combinatorics 6,1 1999
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A. Galluccio, M. Loebl, A Theory of Pfaffian Orientations II Electronic Journal of Combinatorics 6,1 1999
Older publications
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Tamas Fleiner, W. Hochstaettler, M. Laurent, M. Loebl, `Cycle bases For lattices of binary matroids with no Fano dual minor and their one-element extensions', J. Combinatorial Theory B, 77,1 (25-38) 1999
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W.Hochstattler, M. Loebl, `Bases of Cocycle Lattices and Submatrices of a Hadamard Matrix', DIMACS Series in Discrete Mathematics and Theoretical Computer Science 49, AMS 1999
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A. Galluccio, M.Loebl, `Even Cycles and $H$-free Digraphs', Journal of Algorithms 27, 26-41, 1998
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M. Loebl, A. Galluccio, `On the Even Cycle Problem', Zeitschrift fur Angewandte Mathematik und Mechanik, 77-52, 1997
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A. Galluccio, M. Loebl, `(P,Q)-odd Digraphs', Journal of Graph Theory 23, 2 1996, 175-184
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M. Loebl, J. Ne\v set\v ril, `Linearity and Unprovability of Set Union Problem Strategies', SIAM J. of Algorithms 23, 207-230,(1997)
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R.Aharoni, G.T.Herman, M.Loebl, `Jordan Graphs', in Graphical Models and Image Processing 58 (1996), 345-359
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R. Aharoni, M. Loebl, `Strongly Perfect Infinite Graphs', Israel J. of Mathematics 90 (1995), 81-91
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W. Hochstattler, M. Loebl, C. Moll, `Generating Convex Polyominoes at Random', Proceedings of the Fifth
Conference on Formal Power Series and Algebraic Combinatorics, Florence, Italy, 1993, 267 -- 278; Discrete Mathematics 1996 -
A. Galluccio, M.Loebl, `Cycles of Prescribed Modularity', J. of Algorithms 21, 1996, 51-70
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P. Greenberg, M. Loebl, `Strong Connectivity of Polyhedral Complexes', J. of Algebraical Combinatorics 5(1996), 117-125; a French version in: Seminaire de theorie spectrale et geometrie, Chambery-Grenoble 1993
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P. Erd\H os, M. Loebl, V. S\'os, `Discrepancy of Trees', Studia Scientiarum Mathematicarum Hungarica 30(1994)
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A. S. Fraenkel, M. Loebl, `Complexity of Circuit Intersection in Graphs', Discrete Mathematics 141 (1995) 135-151
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M. Loebl, S. Poljak, ` Packing by Families of Subgraphs', Annals of Discrete Mathematics 51, North-Holland 1992, p.181-186
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M. Loebl, S. Poljak, `Efficient Subgraph Packing', J. Comb. Th.(B) 59(1993) 106-121
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A. Galluccio, M. Loebl, `Even/Odd Dipath in Planar Digraphs', Optimization Methods and Software, 1994, 3, 225-236
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M. Loebl, `Gadget Classification', Graphs and Combinatorics (1993) 9, 57-62
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M. Loebl, J. Matousek, `Hercules versus Hidden Hydra Helper', Comm. Math. Univ. Carolinae, 1992
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M. Loebl, `Unprovable Combinatorial Statements', Discrete Mathematics 108 (1992) 333-342
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M. Loebl, J. Ne\v set\v ril, `An Unprovable Ramsey-type Theorem', Proc. Am. Math. Soc. 116, 3 (1992) 819-824
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Y. Crama, M. Loebl, S. Poljak, `A Decomposition of Strongly Unimodular Matrices', Discrete Mathematics 102 (1992),143-147
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M. Loebl, J. Ne\v set\v ril, `Fast and Slow Growing ( A Combinatorial Study of Unprovability)', London Mathematical Society Lecture Note Series 166 (1991), Cambridge University Press
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M. Loebl, S. Poljak, `Subgraph Packing -- a Survey', in Topics in Combinatorics and Graph Theory, Physica-Verlag Heidelberg 1990
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M. Loebl, S. Poljak, `A Hierarchy of Totally Unimodular Matrices', Discrete Mathematics 76(1989).241-246
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A. S. Fraenkel, M. Loebl, J. Ne\v set\v ril, `Epidemiography II: Games With a Dozing Yet Winning Player', J. Comb. Th.(A) 49,1 (1988), 129-143
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M. Loebl, S. Poljak, `On the Union of Matching Matroids', Math. Slovaca 38 (1988), 301-304
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M. Loebl, S. Poljak, `On Matroids Induced by Packing Subgraphs', J. Comb. Th.(B) 44,3 (1988) , 238-354
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M. Loebl, `Extremal Strategies for Hercules and Hydra Game', Comm. Math. Univ. Carolinae 29,1 (1988), 85-95
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M. Loebl, J. Matousek, `On Undecidability of the Weakened Kruskal Theorem', in Contemporary Mathematics vol. 65, AMS 1986, 275-281
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M. Loebl, `Hercules and Hydra, the Game on Rooted Trees', Comm. Math. Univ. Carolinae 26,2 (1985), 259-267
Conference proceedings
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A. Galluccio, M. Loebl, A New algorithm for the max cut problem, Symp. on Discrete Algorithms SODA 1999
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P.E. Haxell, M. Loebl, On Defect Sets in Bipartite Graphs (extended abstract) , ISAAC 1997 334-343
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M. Loebl, `Efficient Maximal Cubic Graphs Cuts', Proceedings 18th International Colloquium on Automata, Languages and Programming (ICALP), 1991
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M. Loebl, J. Ne\v set\v ril, `Postorder Hierarchy for Path Compression and Set Union', Proceedings IMYCS (1988), Lecture Notes in Computer Science (Springer)
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M. Loebl, J. Ne\v set\v ril, `Linearity and Unprovability of the Set Union Problem Strategies (an extended abstract)', Proceedings 20th annual ACM symposium on the theory of computing (STOC), 1988
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M. Loebl, S. Poljak, `Bipartite Packing', in Finite and Infinite Sets, Proceedings of the 7th Hungarian Colloquium on Combinatorics, 1987
Projects
I am coordinating Combinatorial Structures and Processes (CoSP): H2020-MSCA-RISE-2018 project.
I was coordinating Critical Distribution System (CRISDIS): the Czech Ministry of Interior covid motivated project.
The video of my lecture on our progress till June 2021 is available at this link.
Contact
Phone: (+420) 2 2191 4233
Mailing address:
Department of Applied Mathematics
Malostranske namesti 25
118 00 Praha 1
Czech Republic
For electronic correspondence, "loebl" is the user name and "kam.mff.cuni.cz" is the domain name.