The strong chromatic number of a graph

It is shown that there is an absolute constant c with the following property: For any two graphs G1 = (V, E1) and G2 = (V, E2) on the same set of vertices, where G1 has maximum degree at most d and G2 is a vertex disjoint union of cliques of size cd each, the chromatic number of the graph G = (V, E1 U E2) is precisely cd. The proof is based on probabilistic arguments. Copyright © 1992 Wiley Periodicals, Inc., A Wiley Company