On the chromatic number of random graphs

In this paper we consider the classical Erdős–Rényi model of random graphs Gn,p. We show that for p=p(n)⩽n−3/4−δ, for any fixed δ>0, the chromatic number χ(Gn,p) is a.a.s. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2(ℓ−1)log(ℓ−1)⩽p(n−1).