Bipartite graphs with uniquely restricted maximum matchings and their corresponding greedoids

dc.creatorLevit, Vadim E.
dc.creatorMandrescu, Eugen
dc.date2000-11-21
dc.date.accessioned2026-07-07T04:38:43Z
dc.date.available2026-07-07T04:38:43Z
dc.descriptionA maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set if it is a maximum stable set of the subgraph of G spanned by the union of S and 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. One theorem of Nemhauser and Trotter Jr., working as a useful sufficient local optimality condition for the weighted maximum stable set problem, ensures that any local maximum stable set of G can be enlarged to a maximum stable set of G. In one of our previous papers it is proven that the family of all local maximum stable sets of a forest forms a greedoid on its vertex set. In this paper we obtain a generalization of this assertion claiming that the family of all local maximum stable sets of a bipartite graph G is a greedoid if and only if all maximum matchings of G are uniquely restricted.
dc.identifierhttps://arxiv.org/abs/math/0011156
dc.identifierhttp://arxiv.org/abs/math/0011156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60392
dc.subjectCombinatorics
dc.subject05C70, 05C69, 51D10 (Primary) 90C10 (Secondary)
dc.titleBipartite graphs with uniquely restricted maximum matchings and their corresponding greedoids
dc.typetext

Files

Collections