TY - JOUR

T1 - Weighted well-covered claw-free graphs

AU - Levit, Vadim E.

AU - Tankus, David

N1 - Publisher Copyright:
© 2014 Elsevier B.V.

PY - 2015/3/6

Y1 - 2015/3/6

N2 - A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(m32n3) algorithm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality. Assume that a weight function w is defined on the edges of G. Then G is w-equimatchable if all its maximal matchings are of the same weight. For every graph G, the set of weight functions w such that G is w-equimatchable is a vector space. We present an O(m·n4+n5logn) algorithm, which receives an input graph G, and outputs the vector space of weight functions w such that G is w-equimatchable.

AB - A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(m32n3) algorithm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality. Assume that a weight function w is defined on the edges of G. Then G is w-equimatchable if all its maximal matchings are of the same weight. For every graph G, the set of weight functions w such that G is w-equimatchable is a vector space. We present an O(m·n4+n5logn) algorithm, which receives an input graph G, and outputs the vector space of weight functions w such that G is w-equimatchable.

KW - Claw-free graph

KW - Equimatchable graph

KW - Maximal independent set

KW - Maximal matching

KW - Well-covered graph

UR - http://www.scopus.com/inward/record.url?scp=84913570771&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2014.10.008

DO - 10.1016/j.disc.2014.10.008

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AN - SCOPUS:84913570771

SN - 0012-365X

VL - 338

SP - 99

EP - 106

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -