Weighted well-covered graphs without C sub(4), C sub(5), C sub(6), C sub(7)

A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a linear set function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 159; no. 5; pp. 354 - 359
Main Authors Levit, Vadim E, Tankus, David
Format Journal Article
LanguageEnglish
Published 06.03.2011
Subjects
Graphs
Mathematical analysis
Recognition
Vector spaces
Weight function
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Summary:A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a linear set function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same weight. The set of weight functions w for which a graph is w-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is w-well-covered can be done in polynomial time, if the input graph contains neither C sub(4) nor C sub(5) nor C sub(6) nor C sub(7).
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ISSN:0166-218X
DOI:10.1016/j.dam.2010.11.009