Polyhedral Proof of a Characterization of Perfect Bidirected Graphs

Yoshiko T. Ikebe, Akihisa Tamura

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)1000-1007
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE86-A
Issue number5
Publication statusPublished - 2003 May
Externally publishedYes

Fingerprint

Perfect Graphs
Undirected Graph
Graph in graph theory
Polytopes
If and only if

Keywords

  • 0-1 Polytopes
  • Bidirected graphs
  • Degree-two inequalities
  • Perfect graphs

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Information Systems

Cite this

Polyhedral Proof of a Characterization of Perfect Bidirected Graphs. / Ikebe, Yoshiko T.; Tamura, Akihisa.

In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E86-A, No. 5, 05.2003, p. 1000-1007.

Research output: Contribution to journalArticle

@article{9fe2b18d7e63481a838e560c887faab3,
title = "Polyhedral Proof of a Characterization of Perfect Bidirected Graphs",
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 = "0-1 Polytopes, Bidirected graphs, Degree-two inequalities, Perfect graphs",
author = "Ikebe, {Yoshiko T.} and Akihisa Tamura",
year = "2003",
month = "5",
language = "English",
volume = "E86-A",
pages = "1000--1007",
journal = "IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",
issn = "0916-8508",
publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",
number = "5",

}

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

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 -