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

2013/02/27 by Dô Trong Hoang, Hoang, Do Trong, Nguyên Công Minh +3
Computer Science · Mathematics · Medicine · #05C90 #05E40 #05E45 #13D45 #Cholinesterase and Neurodegenerative Diseases #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1302.7076

openalex publication_date 2013/02/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let I(G) be the edge ideal of a simple graph G. In this paper, we will\ngive sufficient and necessary combinatorial conditions of G in which the\nsecond symbolic and ordinary power of its edge ideal are Cohen-Macaulay (resp.\nBuchsbaum, generalized Cohen-Macaulay).\n As an application of our results, we will classify all bipartite graphs in\nwhich the second (symbolic) powers are Cohen-Macaulay (resp. Buchsbaum,\ngeneralized Cohen-Macaulay).\n

Citations

• On local cohomology of a tetrahedral curve

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