# rainbow

## Rainbow AP(4) in an almost equinumerous coloring ★★

Author(s): Conlon

Problem   Do 4-colorings of , for a large prime, always contain a rainbow if each of the color classes is of size of either or ?

Keywords: arithmetic progression; rainbow

## 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