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 $n\to \infty$?