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A maximum stable set in a graph G is a stable set of maximum cardinality. Sis called a local maximum stable set of G if S is a maximum stable set of thesubgraph induced by the closed neighborhood of S. A greedoid (V,F) is called alocal maximum stable set greedoid if there exists a graph G=(V,E) such that itsfamily of local maximum stable sets coinsides with (V,F). It has been shownthat the family local maximum stable sets of a forest T forms a greedoid on itsvertex set. In this paper we demonstrate that if G is a very well-coveredgraph, then its family of local maximum stable sets is a greedoid if and onlyif G has a unique perfect matching.

Local Maximum Stable Sets Greedoids Stemmed from Very Well-Covered Graphs