TY - JOUR

T1 - Polyhedral Proof of a Characterization of Perfect Bidirected Graphs

AU - Ikebe, Yoshiko T.

AU - Tamura, Akihisa

PY - 2003/5

Y1 - 2003/5

N2 - 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.

AB - 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.

KW - 0-1 Polytopes

KW - Bidirected graphs

KW - Degree-two inequalities

KW - Perfect graphs

UR - http://www.scopus.com/inward/record.url?scp=0141903398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141903398&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0141903398

VL - E86-A

SP - 1000

EP - 1007

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 5

ER -