# CIR graphs with no k-clique and no l-independent set

Circle graphs are intersection graphs of chords in a circle. So the vertices are chords of a circle. Two vertices are joint by an edge if the corresponding chords intersects.

 How many vertices can have a circle graph with no \$k\$ clique and no independent set of size \$l\$?

We denote the number of verices by \$c_k_l\$.

• File "k_l.pdf" contains a picture of the largest arrangement of segments with no \$k\$ pairwisely crossing edges and no \$l\$ pairwisely independent edges.
• File "k_l.info" contains log made during the generating of the configurations. It contains the number of configurations with \$n\$ segments and also the duration of computation.
 k\l 2 3 4 5 6 7 8 9 2 1 2_2.pdf 2_2.info 2 2_3.pdf 2_3.info 3 2_4.pdf 2_4.info 4 2_5.pdf 2_5.info 5 2_6.pdf 2_6.info 6 2_7.pdf 2_7.info 7 2_8.pdf 2_8.info 3 2 3_2.pdf 3_2.info 5 3_3.pdf 3_3.info 8 3_4.pdf 3_4.info 12 3_5.pdf 3_5.info 15 3_6.pdf 3_6.info 19 3_7.pdf 3_7.info >22 3_8.pdf 3_8.info 4 3 4_2.pdf 4_2.info 8 4_3.pdf 4_3.info 13 4_4.pdf 4_4.info 19 4_5.pdf 4_5.info 5 4 5_2.pdf 5_2.info 11 5_3.pdf 5_3.info 18 5_4.pdf 5_4.info >22 5_5.pdf 5_5.info 6 5 6_2.pdf 6_2.info 14 6_3.pdf 6_3.info 23 6_4.pdf 6_4.info 7 6 7_2.pdf 7_2.info 17 7_3.pdf 7_3.info 28 7_4.pdf 7_4.info 8 7 8_2.pdf 8_2.info 20 8_3.pdf 8_3.info 33 8_4.pdf 8_4.info 9

You can download program for finding the maximal circle graph with no \$k\$ clique and no \$l\$ independent set (cir_max.tgz).