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A counterexample to the bold conjecture
Author(s) -
Sakuma Tadashi
Publication year - 1997
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199706)25:2<165::aid-jgt8>3.0.co;2-k
Subject(s) - combinatorics , counterexample , conjecture , mathematics , discrete mathematics , graph , simple graph
A pair of vertices (x,y) of a graph G is an o‐critical pair if o( G + xy ) > o( G ), where G + xy denotes the graph obtained by adding the edge xy to G and o(H) is the clique number of H. The o‐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 o‐clique of G, and o‐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 o‐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. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 165–168, 1997