m at h . A C ] 1 N ov 2 00 5 SEQUENTIALLY COHEN - MACAULAY EDGE IDEALS

نویسندگان

  • CHRISTOPHER A. FRANCISCO
  • ADAM VAN TUYL
چکیده

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ 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 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.

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m at h . A C ] 1 2 A pr 2 00 6 SEQUENTIALLY COHEN - MACAULAY EDGE IDEALS

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تاریخ انتشار 2005