An improved algorithm for approximating the chromatic number of Gn, p

Answering a question of Krivelevich and Vu [M. Krivelevich, V.H. Vu, Approximating the independence number and the chromatic number in expected polynomial time, J. Combin. Optimization 6 (2002) 143-155], we present an algorithm for approximating the chromatic number of random graphs Gn, p within a factor of O(√np/ln(np)) in polynomial expected time. The algorithm applies to edge probabilities c0/n ≤ p ≤ 0.99, where c0 > 0 is a certain constant.

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