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The perfection and recognitionof bull-reducible Berge graphs

Published online by Cambridge University Press:  15 March 2005

Hazel Everett ,
Celina M.H. de Figueiredo ,
Sulamita Klein  and
Bruce Reed
Hazel Everett
Affiliation:
LORIA, France; Hazel.Everett@loria.fr
Celina M.H. de Figueiredo
Affiliation:
Universidade Federal do Rio de Janeiro, Brasil; celina@cos.ufrj.br, sula@cos.ufrj.br
Sulamita Klein
Affiliation:
Universidade Federal do Rio de Janeiro, Brasil; celina@cos.ufrj.br, sula@cos.ufrj.br
Bruce Reed
Affiliation:
McGill University, Canada; breed@cs.mcgill.ca
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Abstract

The recently announced Strong Perfect Graph Theorem states that the class ofperfect graphs coincides with the class of graphs containing no inducedodd cycle of length at least 5 or the complement of such a cycle. Agraph in this second class is called Berge. A bull is a graph with fivevertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph isbull-reducible if no vertex is in two bulls. In this paper we give asimple proof that every bull-reducible Berge graph is perfect. Althoughthis result follows directly from the Strong Perfect Graph Theorem, our proofleads to a recognition algorithm for this new class of perfect graphs whosecomplexity, O(n6), is much lower than that announced for perfect graphs.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 145 - 160
Copyright
© EDP Sciences, 2005

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