Regularity Of Edge Ideals Research Articles

Algebraic Properties of Edge Ideals of Some Vertex-Weighted Oriented Cyclic Graphs

We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge. These formulas are functions in the weight of the vertices, and the numbers of edges and cycles. Some examples show that these formulas are related to direction selection and the assumption that [Formula: see text] for any vertex [Formula: see text] cannot be dropped.

The v-number of edge ideals

The aim of this work is to study the v-number of edge ideals of clutters. We relate the v-number with the regularity of edge ideals and classify W2 graphs. If the edge ideal of a graph has second symbolic power Cohen–Macaulay, we show that the graph is edge-critical.

On Betti numbers in the linear strand and regularity of triangular graphs

To every finite simple graph G, we associate the so-called edge ideal I(G), which is a square-free quadratic monomial ideal generated by the monomials corresponding to the edges of G. In this paper, we determine all the initial graded Betti numbers of edge ideals of triangular graphs and alternate triangular graphs in terms of the underlying graph. We also compute the regularity of edge ideals of triangular and alternate triangular graphs.

Projective dimension and regularity of edge ideals of some weighted oriented graphs

We provide formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. We derive from that exact formulas for the depth of those ideals. We also give some examples to show that the assumptions cannot be dropped.

Regularity and projective dimension of edge ideals

ABSTRACTIn this paper, we study the regularity and projective dimension of edge ideals. We provide two upper bounds for the regularity of edge ideals of vertex decomposable graphs in terms of the induced matching number and the number of cycles. Also, we generalize one of the upper bounds given by Dao and Schweig for the projective dimension of hypergraphs.

Bounds on the regularity and projective dimension of ideals associated to graphs

In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.