# Equistable graphs

ArticleinJournal of Graph Theory 18(3):281 - 299 · May 1994with3 Reads
Impact Factor: 0.63 · DOI: 10.1002/jgt.3190180307
Abstract

An equistable graph is a graph for which the incidence vectors of the maximal stable sets are the 0–1 solutions of a linear equation. A necessary condition and a sufficient condition for equistability are given. They are used to characterize the equistability of various classes of perfect graphs, outerplanar graphs, and pseudothreshold graphs. Some classes of equistable graphs are shown to be closed under graph substitution.

• ##### Equistable series - parallel graphs
[Hide abstract] 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 characterize those series-parallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outer-planar graphs.
Full-text · Article · Oct 2003 · Discrete Applied Mathematics
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• ##### Equistable chordal graphs
[Hide abstract] 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 chordal graphs is equistable if and only if every two adjacent non-simplicial vertices have a common simplicial neighbor.
Preview · Article · Oct 2003 · Discrete Applied Mathematics
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• ##### Equistable distance-hereditary graphs
[Hide abstract] ABSTRACT: A graph is called equistable when there is a nonnegativeweight function on its vertices such that a set S of verticeshas total weight 1 if and only if S is maximal stable. We show thata necessary condition for a graph to be equistable is su#cient whenthe graph in question is distance-hereditary. This is used to designa polynomial-time recognition algorithm for equistable distancehereditarygraphs.
Full-text · Article · Feb 2008 · Discrete Applied Mathematics
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