Associated to a simple undirected graph G is a simplicial complex âˆ†G whose faces correspond to the independent sets of G. We call a graph G shellable if âˆ†G is a shellable simplicial complex in theâ€¦ (More)

Let G be a simple undirected graph on n vertices, and let I(G) âŠ† R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proofâ€¦ (More)

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 howâ€¦ (More)

The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We studyâ€¦ (More)

We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial idealâ€¦ (More)

Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) theâ€¦ (More)

Given any finite simplicial complex âˆ†, we show how to construct from a colouring Ï‡ of âˆ† a new simplicial complex âˆ†Ï‡ that is balanced and vertex decomposable. In addition, the h-vector of âˆ†Ï‡ isâ€¦ (More)

Let I = (F 1 ,. .. , Fr) be a homogeneous ideal of the ring R = k[x 0 ,. .. , xn] generated by a regular sequence of type (d 1 ,. .. , dr). We give an elementary proof for an explicit description ofâ€¦ (More)

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 howâ€¦ (More)