# Conditions for β-perfectness

Discussiones Mathematicae Graph Theory (2002)

- Volume: 22, Issue: 1, page 123-148
- ISSN: 2083-5892

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topJudith Keijsper, and Meike Tewes. "Conditions for β-perfectness." Discussiones Mathematicae Graph Theory 22.1 (2002): 123-148. <http://eudml.org/doc/270446>.

@article{JudithKeijsper2002,

abstract = {
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.
},

author = {Judith Keijsper, Meike Tewes},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {chromatic number; colouring number; polynomial time; -perfect graph; coloring number; forbidden subgraph; even hole; claw-free graph},

language = {eng},

number = {1},

pages = {123-148},

title = {Conditions for β-perfectness},

url = {http://eudml.org/doc/270446},

volume = {22},

year = {2002},

}

TY - JOUR

AU - Judith Keijsper

AU - Meike Tewes

TI - Conditions for β-perfectness

JO - Discussiones Mathematicae Graph Theory

PY - 2002

VL - 22

IS - 1

SP - 123

EP - 148

AB -
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.

LA - eng

KW - chromatic number; colouring number; polynomial time; -perfect graph; coloring number; forbidden subgraph; even hole; claw-free graph

UR - http://eudml.org/doc/270446

ER -

## References

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