Critical equimatchable graphs

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dc.authoridEkim, Tinaz/0000-0002-1171-9294en_US
dc.authorwosidEkim, Tinaz/A-3077-2016en_US
dc.contributor.authorDeniz, Zakir
dc.contributor.authorEkim, Tinaz
dc.date.accessioned2024-08-23T16:07:21Z
dc.date.available2024-08-23T16:07:21Z
dc.date.issued2024en_US
dc.departmentDüzce Üniversitesien_US
dc.description.abstractA graph G is equimatchable if every maximal matching of G has the same cardinality. In this paper, we investigate equimatchable graphs such that the removal of any edge creates a graph that is not equimatchable, called edge -critical equimatchable graphs (ECE-graphs). We show that apart from two simple cases, namely bipartite ECE-graphs and even cliques, all ECE-graphs are 2 -connected factor -critical. Accordingly, we give a characterization of factor -critical ECE-graphs with connectivity 2. Our result provides a partial answer to an open question posed by Levit and Mandrescu [Eur. J. Comb. 20 (2019), 261-272] on the characterization of wellcovered graphs with no shedding vertex. We also introduce equimatchable graphs such that the removal of any vertex creates a graph that is not equimatchable, called vertex -critical equimatchable graphs (VCE- graphs). To conclude, we clarify the relationship between various subclasses of equimatchable graphs (including ECE-graphs and VCE-graphs) and discuss the properties of factor -critical ECE-graphs with connectivity at least 3.en_US
dc.description.sponsorshipTUBITAK (The Scientific and Technological Re- search Council of Turkey) [121F018]en_US
dc.description.sponsorshipThis research was supported by TUBITAK (The Scientific and Technological Re- search Council of Turkey) under the project number 121F018. We would like to thank the anonymous referees for their careful reading and constructive comments, which have improved the presentation of this paper.en_US
dc.identifier.endpage193en_US
dc.identifier.issn2202-3518
dc.identifier.startpage171en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12684/14614
dc.identifier.volume88en_US
dc.identifier.wosWOS:001161135600002en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherCentre Discrete Mathematics & Computingen_US
dc.relation.ispartofAustralasian Journal of Combinatoricsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.titleCritical equimatchable graphsen_US
dc.typeArticleen_US

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