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The perfection and recognition of 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; [email protected]
Celina M.H. de Figueiredo
Affiliation:
Universidade Federal do Rio de Janeiro, Brasil; [email protected], [email protected]
Sulamita Klein
Affiliation:
Universidade Federal do Rio de Janeiro, Brasil; [email protected], [email protected]
Bruce Reed
Affiliation:
McGill University, Canada; [email protected]
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Abstract

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

Keywords

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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