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A counterexample to the bold conjecture

✍ Scribed by Sakuma, Tadashi

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 83 KB
Volume: 25
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199706)25:2<165::aid-jgt8>3.0.co;2-k

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✦ Synopsis

A pair of vertices (x, y) of a graph G is an ω-critical pair if ω(G + xy) > ω(G), where G + xy denotes the graph obtained by adding the edge xy to G and ω(H) is the clique number of H. The ω-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 ω-clique of G, and ω-critical pairs within S form a connected graph. In 1993, G. Bacsó raised the following conjecture which implies the famous Strong Perfect Graph Conjecture: If G is a uniquely ω-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.

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