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 …

Let G be a finite simple graph on [n] and I (G)⊂ S the edge ideal of G, where S= K [x 1,…, xn]
is the polynomial ring over a field K. Let m (G) denote the maximum size of matchings of G …

In this paper, we explain the regularity, projective dimension and depth of the edge ideal of
some classes of graphs in terms of invariants of graphs. We show that for a $ C_5 $-free …

Regularity of Squarefree Monomial Ideals | SpringerLink Skip to main content Advertisement
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Let GG be a graph, and let II be the edge ideal of G G. Our main results in this article provide
lower bounds for the depth of the first three powers of II in terms of the diameter of G G. More …

Let $ G $ be a finite simple connected graph on $[n] $ and\[R= K [x_1,\ldots, x_n]\] the
polynomial ring in $ n $ variables over a field $ K $. The edge ideal of $ G $ is the ideal $ I …

This paper is a survey of progress on Stillman's Question: Let J be a homogeneous ideal in
a standard graded polynomial ring over a field. Is there a bound on the projective dimension …

We introduce the concept of edgewise domination in clutters and use it to provide an upper
bound for the projective dimension of any squarefree monomial ideal. We then compare this …

Projective Dimension and Regularity of Powers of Edge Ideals of Vertex-Weighted Rooted
Forests | SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a …

Let $\operatorname {pd}(I (G)) $ and $\operatorname {reg}(I (G)) $ respectively denote the
projective dimension and the regularity of the edge ideal $ I (G) $ of a graph $ G $. For any …