A characterization of well covered graphs of girth 5 or greater
Journal of Combinatorial Theory Series B
Well-covered graphs and extendability
Discrete Mathematics
Well covered simplicial, chordal, and circular arc graphs
Journal of Graph Theory
On 4-connected claw-free well-covered graphs
Discrete Applied Mathematics
Mathematical Structures Underlying Greedy Algorithms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
A new Greedoid: the family of local maximum stable sets of a forest
Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
On α+-stable König-Egerváry graphs
Discrete Mathematics
Local maximum stable sets in bipartite graphs with uniquely restricted maximum matchings
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Triangle-free graphs with uniquely restricted maximum matchings and their corresponding greedoids
Discrete Applied Mathematics
Well-covered graphs and greedoids
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
The Clique Corona Operation and Greedoids
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Graph operations that are good for greedoids
Discrete Applied Mathematics
Extension of the nemhauser and trotter theorem to generalized vertex cover with applications
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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A maximum stable setin a graph G is a stable set of maximum cardinality. The set S is called a local maximum stable set of G, and we write S@?@J(G), if S is a maximum stable set of the subgraph induced by the closed neighborhood of S. A greedoid (V,F) is called a local maximum stable set greedoid if there exists a graph G=(V,E) such that F=@J(G). Nemhauser and Trotter Jr. (1975) [28] proved that any S@?@J(G) is a subset of a maximum stable set of G. In Levit and Mandrescu (2002) [16] we showed that the family @J(T) of a forest T forms a greedoid on its vertex set. The cases where G is bipartite, triangle-free, and well-covered while @J(G) is a greedoid were analyzed in Levit and Mandrescu (2004) [18], Levit and Mandrescu (2007) [20], and Levit and Mandrescu (2008) [23], respectively. In this paper we demonstrate that if G is a very well-covered graph, then the family @J(G) is a greedoid if and only if G has a unique perfect matching.