The complement of a connected bipartite graph is vertex decomposable

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dc.creatorMahmoudi, Mohammad
dc.creatorMousivand, Amir
dc.creatorYassemi, Siamak
dc.date2009-02-25
dc.date.accessioned2026-07-07T12:46:43Z
dc.date.available2026-07-07T12:46:43Z
dc.descriptionAssociated to a simple undirected graph $G$ is a simplicial complex $Δ_G$ whose faces correspond to the independent sets of $G$. A graph $G$ is called vertex decomposable if $Δ_G$ is a vertex decomposable simplicial complex. We are interested in determining what families of graph have the property that the complement of $G$, denoted by $\overline{G}$, is vertex decomposable. We obtain the result that the complement of a connected bipartite graph is vertex decomposable and so it is Cohen-Macaulay due to pureness of $Δ_{\overline{G}}$.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0902.4342
dc.identifierhttp://arxiv.org/abs/0902.4342
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221477
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13H10; 05C75
dc.titleThe complement of a connected bipartite graph is vertex decomposable
dc.typetext

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