The chromatic number of random graphs

Let χ(G(n, p)) denote the chromatic number of the random graphG(n, p). We prove that there exists a constantd ₀ such that fornp(n)>d ₀,p(n)→0, the probability that $$frac{{np}}{{2 log np}}left( {1 + frac{{log log np - 1}}{{log np}}} right)< chi (G(n,p))< frac{{np}}{{2 log np}}left( {1 + frac{{30 log log np}}{{log np}}} right)$$ tends to 1 asn→∞.