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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Do Trong Hoang¹  Nguyen Cong Minh²  Tran Nam Trung¹ 

[1] Inst Math, Hanoi 10307, Vietnam

[2] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

关键词: Symbolic powers;    Edge ideal;    Cohen-Macaulay;    Buchsbaum;    Generalized Cohen-Macaulay;    Bipartite graphs;   

DOI  :  10.1016/j.jcta.2013.02.008

来源: Elsevier

【 摘 要 】

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). Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

【 授权许可】

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