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2008

Well-covered Graphs and Greedoids

14 years 13 days ago
Well-covered Graphs and Greedoids
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 (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 (G) is a greedoid for every forest G. The bipartite graphs and the trianglefree 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 (G) forms a greedoid on its vertex set. In particular, we infer that (G) forms a greedoid for every well-covered graph G of girth at least 6, nonisomorphic to C7.
Vadim E. Levit, Eugen Mandrescu
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where CATS
Authors Vadim E. Levit, Eugen Mandrescu
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