A new approximate graph coloring algorithm

Abstract

Let A be a graph coloring algorithm. Denote by Â(G) the ratio between the maximum number of colors A will use to color the graph C, and the chromatic number of G, χ(G). For most existing polynomial coloring algorithms, Â(G) can be as bad as O(n), where n is the number of vertices in G. The best currently known algorithm guarantees Â(G)-O(n/log n). In this paper we present a simple and efficient coloring algorithm which guarantees Â(G)≤χ(G)n1-1/χ(G)-1, a considerable improvement over the current bounds.