ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 22(1) (2002) 123-148
DOI: 10.7151/dmgt.1163


 Judith Keijsper

University of Twente
Faculty of Mathematical Sciences
7500 AE Enschede, The Netherlands

 Meike Tewes

Freiberg University
Faculty of Mathematics and Computer Sciences
09596 Freiberg, Germany


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.

Keywords: chromatic number, colouring number, polynomial time.

2000 Mathematics Subject Classification: 05C15, 05C75.


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Received 10 August 2000
Revised 3 July 2001