Well-Covered graphs and greedoids

Vadim E. Levit, Eugen Mandrescu Mandrescu

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

4 Scopus citations


G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S 2 a(G), if S is a maximum stable set of the subgraph induced by S [N(S), where N(S) is the neighborhood of S. In 2002 we have proved that a(G) is a greedoid for every forest G. The bipartite graphs and the triangle-free graphs, whose families of local maximum stable sets form greedoids were characterized by Levit and Mandrescu (2003, 2007a). In this paper we demonstrate that if a graph G has a perfect matching consisting of only pendant edges, then a(G) forms a greedoid on its vertex set. In particular, we infer that a(G) forms a greedoid for every well-covered graph G of girth at least 6, non-isomorphic to C 7.

Original languageEnglish
Title of host publicationTheory of Computing 2008 - Proceedings of the Fourteenth Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2008
StatePublished - 2008
EventTheory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008 - Wollongong, NSW, Australia
Duration: 22 Jan 200825 Jan 2008

Publication series

NameConferences in Research and Practice in Information Technology Series
ISSN (Print)1445-1336


ConferenceTheory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008
CityWollongong, NSW


  • Greedoid
  • Local maximum stable set
  • Unique perfect matching
  • Very well-covered graph


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