On relating edges in graphs without cycles of length 4

An edge xy is relating in the graph G if there is an independent set S, containing neither x nor y, such that S∪{x} and S∪{y} are both maximal independent sets in G. It is an NP-complete problem to decide whether an edge is relating [1]. We show that the problem remains NP-complete even for graphs w...

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Bibliographic Details
Published inJournal of discrete algorithms (Amsterdam, Netherlands) Vol. 26; pp. 28 - 33
Main Authors Levit, Vadim E., Tankus, David
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2014
Subjects
Ford and Fulkerson algorithm
Relating edge
SAT problem
Well-covered graph
Ford and Fulkerson algorithm
Relating edge
Well-covered graph
SAT problem
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Summary:An edge xy is relating in the graph G if there is an independent set S, containing neither x nor y, such that S∪{x} and S∪{y} are both maximal independent sets in G. It is an NP-complete problem to decide whether an edge is relating [1]. We show that the problem remains NP-complete even for graphs without cycles of lengths 4 and 5. On the other hand, we show that for graphs without cycles of lengths 4 and 6, the problem can be solved in polynomial time.
ISSN:1570-8667
1570-8675
DOI:10.1016/j.jda.2013.09.007