The chromatic number of a random graph with $o(n^{3/2})$ edges

Let $G(n,m)$ be the Erdos-Renyi random graph with $n$ vertices and $m$ edges and let $δ>0$. Alon and Krivelevich [Combinatorica 1997] proved that for any sequence $m\leq n^{3/2-δ}$ there \emph{exists} an integer sequence $q=q(n)$ such that the chromatic number of $G(n,m)$ equals either $q$ or $q+1$