Some Matching Problems for Bipartite Graphs
Journal of the ACM (JACM)
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
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
On Duality between Local Maximum Stable Sets of a Graph and Its Line-Graph
Graph Theory, Computational Intelligence and Thought
Graph operations that are good for greedoids
Discrete Applied Mathematics
Note: Local maximum stable set greedoids stemming from very well-covered graphs
Discrete Applied Mathematics
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A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈ Ψ (G), if S is a maximum stable set of the subgraph spanned by S U N(S), where N(S) is the neighborhood of S. A matching M is uniquely restricted if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself. Nemhauser and Trotter Jr. (Math. Programming 8(1975) 232-248), proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In Levit and Mandrescu (Discrete Appl. Math., 124 (2002) 91-101) we have shown that the family Ψ(T) of a forest T forms a greedoid on its vertex set. In this paper, we demonstrate that for a bipartite graph G, Ψ(G) is a greedoid on its vertex set if and only if all its maximum matchings are uniquely restricted.