We construct several pairwise-incomparable bounds on the projective dimensions of edge
ideals. Our bounds use combinatorial properties of the associated graphs. In particular, we …

The goal of this paper is to study the structure of the minimal free resolutions associated to a
class of squarefree monomial ideals by using the one-to-one correspondence between …

Abstract Let I= I (G) be the edge ideal of a graph G. We give various general upper bounds
for the regularity function reg Is, for s⩾ 1, addressing a conjecture made by the authors and …

The algebra of basic covers of a graph G, denoted by ̄A(G), was introduced by Herzog as a
suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of …

In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions
are k-step linear; surprisingly, the bounds are logarithmic in the number of variables. We …

The-number of a graded ideal, denoted by, is the minimum degree of a polynomial for which
is a prime ideal. Jaramillo and Villarreal (J Combin Theory Ser A 177: 105310, 2021) …

Let G be a graph which belongs to either of the following classes:(i) bipartite graphs,(ii)
unmixed graphs, or (iii) claw–free graphs. Assume that J (G) is the cover ideal G and J …

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 …

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some
classes of graphs. We compute the depth of the binomial edge ideal of a generalized block …

Inspired by several recent papers on the edge ideal of a graph $ G $, we study the
equivalent notion of the independence complex of $ G $. Using the tool of vertex …