1-well-covered graphs containing a clique of size n/3

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dc.contributor.authorDeniz, Zakir
dc.date.accessioned2025-10-11T20:47:36Z
dc.date.available2025-10-11T20:47:36Z
dc.date.issued2024
dc.departmentDüzce Üniversitesien_US
dc.description.abstractA graph is well-covered if all of its maximal independent sets have the same size. A graph that remains well-covered upon the removal of any vertex is called a 1-well-covered graph. These graphs, when they have no isolated vertices, are also known as W-2 graphs. It is well-known that every graph G is an element of W-2 has two disjoint maximum independent sets. In this paper, we investigate connected W-2 graphs with n vertices that contain a clique of size n/3. We prove that if the removal of two disjoint maximum independent sets from a graph G is an element of W-2 leaves a clique of size at least 3, then G contains a clique of size n/3. Using this result, we provide a complete characterization of these graphs, based on eleven graph families.en_US
dc.description.sponsorshipTUBITAK (The Scientific and Technological Research Council of Turkey) [121F018]en_US
dc.description.sponsorshipAcknowledgement This research was supported by TUBITAK (The Scientific and Technological Research Council of Turkey) under the project number 121F018. The author thanks the anonymous referee for their careful reading and invaluable comments.en_US
dc.identifier.doi10.5614/ejgta.2024.12.2.8
dc.identifier.endpage288en_US
dc.identifier.issn2338-2287
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85212226717en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage273en_US
dc.identifier.urihttps://doi.org/10.5614/ejgta.2024.12.2.8
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21460
dc.identifier.volume12en_US
dc.identifier.wosWOS:001354040100008en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorDeniz, Zakir
dc.language.isoenen_US
dc.publisherInst Teknologi Bandungen_US
dc.relation.ispartofElectronic Journal of Graph Theoryand Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectindependent seten_US
dc.subjectcliqueen_US
dc.subjectmatchingen_US
dc.subjectwell-covereden_US
dc.title1-well-covered graphs containing a clique of size n/3en_US
dc.typeArticleen_US

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