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The Chromatic Number of Random Regular Graphs

Dimitris Achlioptas·Cristopher Moore
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Abstract

Given any integer d >= 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k+1, or k+2, and that if (2k-1) \log k < d < 2k \log k then the chromatic number is either k+1 or k+2.

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Dimitris Achlioptas, Cristopher Moore. 2004-07-11. The Chromatic Number of Random Regular Graphs. https://arxiv.org/abs/cond-mat/0407278

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