A β-perfect graph is a simple graph G such that χ(G') = β(G') for every induced subgraph G' of G, where χ(G') is the chromatic number of G', and β(G') is defined as the maximum over all induced subgraphs H of G' of the minimum vertex degree in H plus 1 (i.e., δ(H)+1). The vertices of a β-perfect graph G can be coloured with χ(G) colours in polynomial time (greedily). The main purpose of this paper is to give necessary and sufficient conditions, in terms of forbidden induced subgraphs, for a graph to be β-perfect. We give new sufficient conditions and make improvements to sufficient conditions previously given by others. We also mention a necessary condition which generalizes the fact that no β-perfect graph contains an even hole.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1163,
author = {Judith Keijsper and Meike Tewes},
title = {Conditions for $\beta$-perfectness},
journal = {Discussiones Mathematicae Graph Theory},
volume = {22},
year = {2002},
pages = {123-148},
zbl = {1010.05032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1163}
}
Judith Keijsper; Meike Tewes. Conditions for β-perfectness. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 123-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1163/
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