We show that the co-chordal cover number of a graph 𝐺 gives an upper bound for the
Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial …

Let $ G $ be a graph with $ n $ vertices and $ S=\mathbb {K}[x_1,\dots, x_n] $ be the
polynomial ring in $ n $ variables over a field $\mathbb {K} $. Assume that $ J (G) $ is the …

A graph is called very well-covered if it is unmixed without isolated vertices such that the
cardinality of each minimal vertex cover is half the number of vertices. We first prove that a …

We survey recent studies on the Castelnuovo–Mumford regularity of edge ideals of graphs
and their powers. Our focus is on bounds and exact values of reg I (G) reg I (G) and the …

The Castelnuovo–Mumford regularity of binomial edge ideals - ScienceDirect Skip to main
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REGULARITY BOUNDS FOR BINOMIAL EDGE IDEALS 1. Introduction. Let G be a simple
graph on the vertex set [n] = {1, 2,... ,n}. The b Page 1 JOURNAL OF COMMUTATIVE …

Let G be a finite simple graph and I (G) denote the corresponding edge ideal. In this paper,
we obtain upper bounds for the Castelnuovo-Mumford regularity of I (G) q in terms of certain …

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 …

In a 2008 paper, the first author and Van Tuyl proved that the regularity of the edge ideal of a
graph G is at most one greater than the matching number of G. In this note, we provide a …

Let C be a clutter and let IC/ R be its edge ideal. This is a survey paper on the algebraic and
combinatorial properties of R= IC/and C, respectively. We give a criterion to estimate the …