Polyhedral Proof of a Characterization of Perfect Bidirected Graphs

Yoshiko T. IKEBE  Akihisa TAMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.5   pp.1000-1007
Publication Date: 2003/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
bidirected graphs,  degree-two inequalities,  0-1 polytopes,  perfect graphs,  

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Bidirected graphs which are generalizations of undirected graphs, have three types of edges: (+,+)-edges, (-,-)-edges and (+,-)-edges. Undirected graphs are regarded as bidirected graphs whose edges are all of type (+,+). The notion of perfection of undirected graphs can be naturally extended to bidirected graphs in terms of polytopes. The fact that a bidirected graph is perfect if and only if the undirected graph obtained by replacing all edges to (+,+) is perfect was independently proved by several researchers. This paper gives a polyhedral proof of the fact and introduces some new knowledge on perfect bidirected graphs.