Equistable distance-hereditary graphs

Ephraim Korach; Uri N. Peled; Udi Rotics

doi:10.1016/j.dam.2006.06.018

Equistable distance-hereditary graphs

Ephraim Korach
, Uri N. Peled
, Udi Rotics

Department of Industrial Engineering and Management

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distance-hereditary graphs.

Original language	English
Pages (from-to)	462-477
Number of pages	16
Journal	Discrete Applied Mathematics
Volume	156
Issue number	4
DOIs	https://doi.org/10.1016/j.dam.2006.06.018
State	Published - 15 Feb 2008

Keywords

Distance-hereditary graphs
Equistable graphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2006.06.018

Cite this

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title = "Equistable distance-hereditary graphs",

abstract = "A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distance-hereditary graphs.",

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AU - Korach, Ephraim

AU - Peled, Uri N.

AU - Rotics, Udi

PY - 2008/2/15

Y1 - 2008/2/15

N2 - A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distance-hereditary graphs.

AB - A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distance-hereditary graphs.

KW - Distance-hereditary graphs

KW - Equistable graphs

UR - https://www.scopus.com/pages/publications/38149051226

U2 - 10.1016/j.dam.2006.06.018

DO - 10.1016/j.dam.2006.06.018

M3 - Article

AN - SCOPUS:38149051226

SN - 0166-218X

VL - 156

SP - 462

EP - 477

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 4

ER -

Equistable distance-hereditary graphs

Abstract

Keywords

ASJC Scopus subject areas

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