Almost all graphs with average degree 4 are 3-colorable

Authors:
Dimitris Achlioptas;Cristopher Moore
Affiliations:
Microsoft Research, Redmond, Washington;Computer Science Department, University of New Mexico, Farris Engineering Center, Albuquerque, NM and Santa Fe Institute, Santa Fe, NM
Venue:
Journal of Computer and System Sciences - STOC 2002
Year:
2003

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Abstract

We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree d ≤ 4.03, i.e., G(n,p = d/n), are 3-colorable and that a constant fraction of all 4-regular graphs are 3-colorable.