Sequential and distributed graph coloring algorithms with performance analysis in random graph spaces

A sequential graph coloring algorithm S and a strict distributed (broadcasting type) algorithm D, and an analysis of their performance in scales of random graph spaces is presented. For a space of graphs with n vertices and a mean degree d(n), the number of colors produced is almost surely bounded by about d(n) logd(n), which is almost surely not more than twice the chromatic number, and the distributed algorithm terminates in O(Max(d(n),logn)) steps.