منابع مشابه
Totally equimatchable graphs
A subset X of vertices and edges of a graph G is totally matching if no two elements of X are adjacent or incident. In this paper we determine all graphs in which every maximal total matching is maximum.
متن کاملEquimatchable Claw-Free Graphs
A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable clawfree graph families. This characterization implies an efficient recognition algorithm.
متن کاملStable Equimatchable Graphs
A graph G is equimatchable if every maximal matching of G has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph G edge-stable if G\e is equimatchable for any e ∈ E(G). After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartit...
متن کاملEquimatchable Graphs on Surfaces
A graph G is equimatchable if any matching of G is a subset of a maximum-size matching. From a general description of equimatchable graphs in terms of GallaiEdmonds decomposition [Lesk, Plummer, and Pulleyblank, "Equimatchable graphs", Graphs Theory and Combinatorics, Academic press, London, (1984) 239-254.] it follows that any 2-connected equimatchable graph is either bipartite or factor-criti...
متن کاملA note on equimatchable graphs
Let G = (V, E) be a graph. A set M of edges is called a matching in G if each vertex in G belongs to at most one edge from M , and M is a maximal matching if any edgeset M ′, such that M ⊂ M ′, is not a matching in G. If all maximal matchings in G have the same cardinality then G is an equimatchable graph. In this paper we characterize the equimatchable graphs of girth at least five. As a conse...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00062-3