Graph Operations that are Good for Greedoids
نویسندگان
چکیده
S is a local maximum stable set of G, and we write S 2 (G), if S is a maximum stable set of the subgraph induced by S [N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [5] proved that any S 2 (G) is a subset of a maximum stable set of G. In [1] we have proved that (G) is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in [2] and [3], respectively. If G has a perfect matching consisting of only pendant edges, then (G) forms a greedoid on its vertex set, i.e., (G) is a greedoid for every well-covered graph G of girth at least 6, non-isomorphic to C7, [4]. In this paper we present necessary and su¢ cient conditions for (G) to form a greedoid, where G is the disjoint union of a family of graphs, the Zykov sum of a family of graphs, or is obtainned by joining each vertex x of a graph X to all the vertices of a graph Hx.
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 158 شماره
صفحات -
تاریخ انتشار 2010