Mathematics – Combinatorics
Scientific paper
2008-09-10
Mathematics
Combinatorics
8 pages, 4 figures
Scientific paper
S is a local maximum stable set of a graph G, if the set S is a maximum stable set of the subgraph induced by its closed neighborhood. In (Levit, Mandrescu, 2002) we have proved that the family of all local maximum stable sets is a greedoid for every forest. The cases of bipartite graphs and triangle-free graphs were analyzed in (Levit, Mandrescu, 2004) and (Levit, Mandrescu, 2007), respectively. In this paper we give necessary and sufficient conditions for the family of all local maximum stable sets of a graph G to form a greedoid, where G is: (a) the disjoint union of a family of graphs; (b) the Zykov sum of a family of graphs, or (c) the corona X*{H_1,H_2,...,H_n} obtained by joining each vertex k of a graph X to all the vertices of a graph H_k.
Levit Vadim E.
Mandrescu Eugen
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