Weighted well-covered graphs without C4, C5, C 6, C7

Vadim E. Levit, David Tankus

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 C4 nor C5 nor C6 nor C7.

Original languageEnglish
Pages (from-to)354-359
Number of pages6
JournalDiscrete Applied Mathematics
Issue number5
StatePublished - 6 Mar 2011


  • Generating subgraph
  • Hereditary system
  • Independent set
  • Relating edge
  • Well-covered graph


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