The two possible values of the chromatic number of a random graph

Authors:
Dimitris Achlioptas;Assaf Naor
Affiliations:
Microsoft Research, Redmond, WA;Microsoft Research, Redmond, WA
Venue:
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Year:
2004

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Abstract

For every d 0, let kd be the smallest integer k such that d d or kd+1 almost surely. If d ∈ (2k log k - log k, 2k log k) we further prove that the chromatic number almost surely equals k+1.