The chromatic number of random graphs

Abstract

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→∞.