On duality between local maximum stable sets of a graph and its line-graph

Vadim E. Levit, Eugen Mandrescu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


G is a König-Egervá ry graph provided α(G)+μ(G) = |V (G)|, where μ(G) is the size of a maximum matching and α(G) is the cardinality of a maximum stable set,[2],[21]. S is a local maximum stable set of G, and we write S ∈Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S,[11]. Nemhauser and Trotter Jr. proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G,[19]. In this paper we demonstrate that if S∈ Ψ(G), the subgraph H induced by S ∪ N(S) is a König-Egerváry graph, and M is a maximum matching in H, then M is a local maximum stable set in the line graph of G.

Original languageEnglish
Title of host publicationGraph Theory, Computational Intelligence and Thought - Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday
EditorsMarina Lipshteyn, Vadim E. Levit, Ross M. McConnell
Number of pages7
StatePublished - 2009
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5420 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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