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

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 …

Monomial ideals, although intrinsically interesting, play an important role in studying the
connections between commutative algebra and combinatorics. Broadly speaking, problems …

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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 …

In this paper we study the Alexander dual of a vertex decomposable simplicial complex. We
define the concept of a vertex splittable ideal and show that a simplicial complex Δ is vertex …

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 …

Given a finite simple graph, one can associate the edge ideal. In this article, we prove that a
graded Betti number of the edge ideal does not vanish if the original graph contains a set of …

Monomial ideals and algebras are among the simplest structures in commutative algebra
and the main objects in combinatorial commutative algebra. One can highlight several …

The shedding vertices of simplicial complexes are studied from an algebraic point of view.
Based on this perspective, we introduce the class of ass-decomposable monomial ideals …