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dc.contributor.authorBıyıkoğlu, Türker
dc.contributor.authorCivan, Yusuf
dc.date.accessioned2017-05-24T11:16:20Z
dc.date.available2017-05-24T11:16:20Z
dc.date.issued2014-01
dc.identifier.citationBıyıkoğlu, T., and Civan, Y. (2014). Vertex-decomposable graphs, codismantlability, cohen-macaulayness, and castelnuovo-mumford regularity. Electronic Journal of Combinatorics, 21(1).en_US
dc.identifier.issn1077-8926
dc.identifier.urihttp://hdl.handle.net/11147/5597
dc.description.abstractWe call a vertex x of a graph G = (V, E) a codominated vertex if NG[y] ⊆ NG[x] for some vertex y ∈ V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G - x is codismantlable. We show that (C4, C5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C4, C5, C7)-free well-covered graph, then vertex-decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. These results complement and unify many of the earlier results on bipartite, chordal and very well-covered graphs. We also study the Castelnuovo-Mumford regularity reg(G) of such graphs, and show that reg(G) = im(G) whenever G is a (C4, C5)-free vertex-decomposable graph, where im(G) is the induced matching number of G. Furthermore, we prove that H must be a codismantlable graph if im(H) = reg(H) = m(H), where m(H) is the matching number of H. We further describe an operation on digraphs that creates a vertex-decomposable and codismantlable graph from any acyclic digraph. By way of application, we provide an infinite family Hn (n ≥ 4) of sequentially Cohen-Macaulay graphs whose vertex cover numbers are half of their orders, while containing no vertex of degree-one such that they are vertex-decomposable, and reg(Hn) = im(Hn) if n ≥ 6. This answers a recent question of Mahmoudi, et al [12].en_US
dc.language.isoengen_US
dc.publisherElectronic Journal of Combinatoricsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectEdge ringsen_US
dc.subjectVertex decomposable graphsen_US
dc.subjectInduced matchingen_US
dc.subjectCodismantlabilityen_US
dc.subjectCochordal cover numberen_US
dc.titleVertex-decomposable graphs, codismantlability, cohen-macaulayness, and castelnuovo-mumford regularityen_US
dc.typearticleen_US
dc.contributor.iztechauthorBıyıkoğlu, Türker
dc.relation.journalElectronic Journal of Combinatoricsen_US
dc.contributor.departmentİYTE, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume21en_US
dc.identifier.issue1en_US
dc.identifier.scopusSCOPUS:2-s2.0-84892605087
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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