# Fox, Jacob

## Separators in string graphs ★★

**Conjecture**Every string graph with edges has a separator of size .

Keywords: separator; string graphs

## 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