dc.contributor.author Bıyıkoğlu, Türker dc.contributor.author Civan, Yusuf dc.date.accessioned 2017-05-24T11:16:20Z dc.date.available 2017-05-24T11:16:20Z dc.date.issued 2014-01 dc.identifier.citation Bıyıkoğlu, 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.issn 1077-8926 dc.identifier.uri http://hdl.handle.net/11147/5597 dc.description.abstract We 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.iso eng en_US dc.publisher Electronic Journal of Combinatorics en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Edge rings en_US dc.subject Vertex decomposable graphs en_US dc.subject Induced matching en_US dc.subject Codismantlability en_US dc.subject Cochordal cover number en_US dc.title Vertex-decomposable graphs, codismantlability, cohen-macaulayness, and castelnuovo-mumford regularity en_US dc.type article en_US dc.contributor.iztechauthor Bıyıkoğlu, Türker dc.relation.journal Electronic Journal of Combinatorics en_US dc.contributor.department İYTE, Fen Fakültesi, Matematik Bölümü en_US dc.identifier.volume 21 en_US dc.identifier.issue 1 en_US dc.identifier.scopus SCOPUS:2-s2.0-84892605087 dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
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