The Chromatic Number of Random Regular Graphs
Disordered Systems and Neural Networks
2007-05-23 v1 Statistical Mechanics
Combinatorics
Probability
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.
Cite
@article{arxiv.cond-mat/0407278,
title = {The Chromatic Number of Random Regular Graphs},
author = {Dimitris Achlioptas and Cristopher Moore},
journal= {arXiv preprint arXiv:cond-mat/0407278},
year = {2007}
}