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The perfection and recognition of bull-reducible Berge graphs

Hazel Everett; Celina M.H. de Figueiredo; Sulamita Klein; Bruce Reed — 2010

RAIRO - Theoretical Informatics and Applications

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 and five edges . 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 perfection and recognition of bull-reducible Berge graphs

Hazel Everett; Celina M. H. de Figueiredo; Sulamita Klein; Bruce Reed — 2005

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 $x a, x b, a b, a d, b c$ . 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...