Critical equimatchable graphs

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dc.authorscopusid56462806000en_US
dc.authorscopusid9632804500en_US
dc.contributor.authorDeniz, Z.
dc.contributor.authorEkim, T.
dc.date.accessioned2024-08-23T16:07:41Z
dc.date.available2024-08-23T16:07:41Z
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 well-covered 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 (VCEgraphs). 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. © The author(s).en_US
dc.description.sponsorshipTürkiye Bilimsel ve Teknolojik Araştırma Kurumu, TÜBİTAK, (121F018)en_US
dc.identifier.endpage193en_US
dc.identifier.issn1034-4942
dc.identifier.scopus2-s2.0-85184456988en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage171en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12684/14785
dc.identifier.volume88en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherUniversity of Queenslanden_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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