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Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals

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 نشر من قبل Cong Minh Nguyen
 تاريخ النشر 2013
  مجال البحث
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Let $I(G)$ be the edge ideal of a simple graph $G$. In this paper, we will give sufficient and necessary combinatorial conditions of $G$ in which the second symbolic and ordinary power of its edge ideal are Cohen-Macaulay (resp. Buchsbaum, generalized Cohen-Macaulay). As an application of our results, we will classify all bipartite graphs in which the second (symbolic) powers are Cohen-Macaulay (resp. Buchsbaum, generalized Cohen-Macaulay).



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