@article {1501,
	title = {Edge-stable equimatchable graphs},
	journal = {Discrete Applied Mathematics},
	volume = {261},
	year = {2019},
	pages = {136-147},
	abstract = {<p>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, 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.</p>},
	keywords = {1-well-covered, Edge-criticality, Edge-stability, Maximal matching, Shedding vertex},
	issn = {0166-218X},
	doi = {https://doi.org/10.1016/j.dam.2018.09.033},
	url = {https://www.sciencedirect.com/science/article/pii/S0166218X18305158},
	author = {Zakir Deniz and Ekim, Tinaz}
}
