rainbow

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

Author(s): Conlon

Problem Do 4-colorings of $\mathbb{Z}_{p}$ , for $p$ a large prime, always contain a rainbow $AP(4)$ if each of the color classes is of size of either $\lfloor p/4\rfloor$ or $\lceil p/4\rceil$ ?

Keywords: arithmetic progression; rainbow

Posted by vjungic
updated September 1st, 2007

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Combinatorics

Long rainbow arithmetic progressions ★★

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

For $k\in \mathbb{N}$ let $T_k$ denote the minimal number $t\in \mathbb{N}$ such that there is a rainbow $AP(k)$ in every equinumerous $t$ -coloring of $\{ 1,2,\ldots ,tn\}$ for every $n\in \mathbb{N}$