Optimality of DSatur algorithm on chordal graphs

Abstract

DSatur is a widely-used heuristic algorithm for graph coloring, proposed by Daniel Brélaz in 1979. It is based on the greedy coloring approach, but selecting the next vertex to be colored from those that maximize the number of colors already used by their neighbors. Though not always optimal, this algorithm is known to be optimal on certain families, like cycles or bipartite graphs. In this paper, we prove the optimality of DSatur on chordal graphs, a superclass of interval graphs.