TY - GEN

T1 - Well-Covered graphs and greedoids

AU - Levit, Vadim E.

AU - Mandrescu, Eugen Mandrescu

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Greedoid

KW - Local maximum stable set

KW - Unique perfect matching

KW - Very well-covered graph

UR - http://www.scopus.com/inward/record.url?scp=84863562612&partnerID=8YFLogxK

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AN - SCOPUS:84863562612

SN - 9781920682583

T3 - Conferences in Research and Practice in Information Technology Series

BT - Theory of Computing 2008 - Proceedings of the Fourteenth Computing

T2 - Theory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008

Y2 - 22 January 2008 through 25 January 2008

ER -