Combinatorial properties of the family of maximum stable sets of a graph

On α + -stable König-Egerváry graphs

A matching M is called uniquely restricted in a graph G if it is the unique perfect matching of the subgraph induced by the vertices that M saturates. G is a unicycle graph if it owns only one cycle.

Unicycle Bipartite Graphs with Only Uniquely Restricted Maximum Matchings

A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, if S is a maximum stable set of the subgraph induced by its closed neighborhood. 
It is known that the family of all local maximum stable sets of a forest forms a greedoid on its vertex set. Bipartite, triangle-free, and well-covered graphs whose families of local maximum stable sets form greedoids have been analyzed as well. 
A unicycle graph owns only one cycle. In this paper we characterize the unicycle graphs whose families of local maximum stable sets form greedoids.

Greedoids on Vertex Sets of Unicycle Graphs.

Local maximum stable set greedoids stemming from very well-covered graphs

On the structure of a-stable graphs

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On the structure of a-stable graphs