On the chromatic number of random graphs

Authors:
Amin Coja-Oghlan;Konstantinos Panagiotou;Angelika Steger
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA;Institute of Theoretical Computer Science ETH Zentrum, Zurich, Switzerland;Institute of Theoretical Computer Science ETH Zentrum, Zurich, Switzerland
Venue:
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Year:
2007

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Abstract

In this paper we study the chromatic number χ(Gn,p) of the binomial random graph Gn,p, where p = p(n) ≤ n-3/4-δ, for every fixed δ 0. We prove that a.a.s. χ(Gn,p) is l, l + 1, or l + 2, where l is the maximum integer satisfying 2(l - 1) log(l - 1) ≤ np.