Clique-chromatic number of dense random graphs

Yury Demidovich, Maksim Zhukovskii

Published 2020-12-06Version 1

The clique chromatic number of a graph is the minimum number of colors required to assign to its vertex set so that no inclusion maximal clique is monochromatic. McDiarmid, Mitsche and Pra\l at proved that the clique chromatic number of the binomial random graph $G\left(n,\frac{1}{2}\right) $ is at most $\left(\frac{1}{2}+o(1)\right)\log_2n$ with high probability. Alon and Krivelevich showed that it is greater than $\frac{1}{2000}\log_2n$ with high probability. In this paper we show that the upper bound is asymptotically tight.