A COUNTEREXAMPLE TO THE BOLD CONJECTURE

摘要

A pair of vertices (x, y) of a graph G is an w-critical pair if w(G + xy) > w (G), where G + xy denotes the graph obtained by adding the edge xy to G and w(H) is the clique number of H. The w-critical pairs are never edges in G. A maximal stable set S of G is called a forced color class of G if S meets every w-clique of G, and w-critical pairs within S form a connected graph. In 1993, G. Bacso raised the following conjecture which implies the famous Strong Perfect Graph Conjecture: If G is a uniquely w-colorable perfect graph, then G has at least one forced color class, This conjecture is called the Bold Conjecture. Here we show a simple counterexample to it. (C) 1997 John Wiley & Sons, Inc. [References: 6]