منابع مشابه
Regularity of edge ideals of C4-free graphs via the topology of the lcm-lattice
We study the topology of the lcm-lattice of edge ideals and derive upper bounds on the Castelnuovo-Mumford regularity of the ideals. In this context it is natural to restrict to the family of graphs with no induced 4-cycle in their complement. Using the above method we obtain sharp upper bounds on the regularity when the complement is a chordal graph, or a cycle, or when the original graph is c...
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Let $X=left( begin{array}{llll} x_1 & ldots & x_{n-1}& x_n\ x_2& ldots & x_n & x_{n+1} end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...
متن کاملMonomial Ideals, Edge Ideals of Hypergraphs, and Their Minimal Graded Free Resolutions
We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph H appears within the resolution of its edge ideal I(H). We discuss when recursive formulas to compute the graded Betti numbers of I(H) in terms of its sub...
متن کاملRegularity of second power of edge ideals
Let G be a graph with edge ideal I(G). Benerjee and Nevo proved that for every graph G, the inequality reg(I(G)2)≤reg(I(G))+2 holds. We provide an alternative proof for this result.
متن کاملSequentially Cohen-macaulay Edge Ideals
Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] 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 impl...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2012
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-012-0364-2