Edge-stable 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 Gedge-stable if G∖e, that is the graph obtained by the removal...
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| Veröffentlicht in: | Discrete Applied Mathematics 2019-05, Vol.261, p.136-147 |
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| creator | Deniz, Zakir Ekim, Tınaz |
| description | 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 Gedge-stable if G∖e, that is the graph obtained by the removal of edge e from G, is also equimatchable for any e∈E(G). After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartite, we characterize edge-stable equimatchable graphs. This characterization yields an O(min(n3.376,n1.5m)) time recognition algorithm. Lastly, we introduce and shortly discuss the related notions of edge-critical, vertex-stable and vertex-critical equimatchable graphs. In particular, we emphasize the links between our work and the well-studied notion of shedding vertices, and point out some open questions. |
| doi_str_mv | 10.1016/j.dam.2018.09.033 |
| format | Article |
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| ispartof | Discrete Applied Mathematics, 2019-05, Vol.261, p.136-147 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | 1-well-covered Algorithms Apexes Edge-criticality Edge-stability Graphs Maximal matching Shedding vertex |
| title | Edge-stable equimatchable graphs |
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