The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

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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 …

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 …

A very well–covered graph is an unmixed graph without isolated vertices such that the
height of its edge ideal is half of the number of vertices. We study these graphs by means of …

Let G be a finite simple graph and I (G) denote the corresponding edge ideal. For all s ≥ 1
s≥ 1, we obtain upper bounds for reg (I (G)^ s) reg (I (G) s) for bipartite graphs. We then …

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 …

We study the relationship between depth and regularity of a homogeneous ideal I and those
of (I, f) and I: f, where f is a linear form or a monomial. Our results have several interesting …

We give a formula for the v-number of a graded ideal that can be used to compute this
number. Then, we show that for the edge ideal I (G) of a graph G, the induced matching …

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 …