Clique coloring of binomial random graphs

A clique coloring of a graph is a coloring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colors in such a coloring is the clique chromatic number. In this paper, we study the asymptotic behavior of the clique chromatic number of the random graph G(n,p) for a wide range of edge-probabilities p = p(n). We see that the typical clique chromatic number, as a function of the average degree, forms an intriguing step function.