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
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
Note: Local maximum stable set greedoids stemming from very well-covered graphs
Discrete Applied Mathematics
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S is a local maximum stable set of a graph G, and we write S@?@J(G), if the set S is a maximum stable set of the subgraph induced by S@?N(S), where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that @J(G) is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively. In this paper we give necessary and sufficient conditions for @J(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; (c)the corona X@?{H"1,H"2,...,H"n} obtained by joining each vertex x of a graph X to all the vertices of a graph H"x.