Polyhedral Proof of a Characterization of Perfect Bidirected Graphs

Yoshiko T. IKEBE; Akihisa TAMURA

Polyhedral Proof of a Characterization of Perfect Bidirected Graphs

Yoshiko T. IKEBE, Akihisa TAMURA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.5 pp.1000-1007

Publication Date: 2003/05/01

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Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Yoshiko T. IKEBE, Akihisa TAMURA, "Polyhedral Proof of a Characterization of Perfect Bidirected Graphs" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 5, pp. 1000-1007, May 2003, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_5_1000/_p

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@ARTICLE{e86-a_5_1000,
author={Yoshiko T. IKEBE, Akihisa TAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Polyhedral Proof of a Characterization of Perfect Bidirected Graphs},
year={2003},
volume={E86-A},
number={5},
pages={1000-1007},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Polyhedral Proof of a Characterization of Perfect Bidirected Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1000
EP - 1007
AU - Yoshiko T. IKEBE
AU - Akihisa TAMURA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2003
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.
ER -