Fox, Jacob

Complete bipartite subgraphs of perfect graphs ★★

Author(s): Fox

Problem   Let be a perfect graph on vertices. Is it true that either or contains a complete bipartite subgraph with bipartition so that ?

Keywords: perfect graph

Long rainbow arithmetic progressions ★★

Author(s): Fox; Jungic; Mahdian; Nesetril; Radoicic

For let denote the minimal number such that there is a rainbow in every equinumerous -coloring of for every

Conjecture   For all , .

Keywords: arithmetic progression; rainbow