Achlioptas, Dimitris; Moore, Cristopher - Santa Fe Institute - 2001
of the practically successful Brelaz heuristic. This allows to prove that almost all graphs with average degree $d$, i ….e. $G(n,p=d/n)$, are 3-colorable for $d \leq 4.03$, and that almost all 4-regular graphs are 3-colorable. This improves over …-trivial result on the colorability of random regular graphs. In fact, our methods can be used to deal with "arbitrary" sparse degree …