Trivial colors in colorings of Kneser graphs

12/28/2020

∙

by   Sergei Kiselev, et al.

∙

0

∙

share

We show that any proper coloring of a Kneser graph KG_n,k with n-2k+2 colors contains a trivial color (i.e., a color consisting of sets that all contain a fixed element), provided n>(2+ϵ)k^2, where ϵ→ 0 as k→∞. This bound is essentially tight.