Sequentially Cohen-Macaulay Edge Ideals

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dc.creatorFrancisco, Christopher A.
dc.creatorVan Tuyl, Adam
dc.date2005-11-01
dc.date2006-04-12
dc.date.accessioned2026-07-07T08:07:21Z
dc.date.available2026-07-07T08:07:21Z
dc.descriptionLet G be a simple undirected graph on n vertices, and let I(G) \subseteq R = k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and implies Herzog, Hibi, and Zheng's theorem that a chordal graph is Cohen-Macaulay if and only if its edge ideal is unmixed. We also characterize the sequentially Cohen-Macaulay cycles and produce some examples of nonchordal sequentially Cohen-Macaulay graphs.
dc.description11 pages; revised, final version; to appear in Proc. AMS
dc.identifierhttps://arxiv.org/abs/math/0511022
dc.identifierhttp://arxiv.org/abs/math/0511022
dc.identifierProc. Amer. Math. Soc. 135 (2007), no. 8, 2327-2337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130913
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13F55; 13D02; 05C38; 05C75
dc.titleSequentially Cohen-Macaulay Edge Ideals
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