Historically, commutative algebra, whose foundations were laid by Dedekind, Hilbert,
Noether, and Krull, has developed in step with algebraic geometry, number theory …

The Castelnuovo–Mumford regularity of binomial edge ideals - ScienceDirect Skip to main
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We study the regularity of binomial edge ideals. For a closed graph G we show that the
regularity of the binomial edge ideal coincides with the regularity of and can be expressed in …

Let G be a finite simple graph on n vertices and JG denote the corresponding binomial edge
ideal in S= K [x 1,…, xn, y 1,…, yn]. We compute the Castelnuovo-Mumford regularity of S/JG …

In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a
graph G, we define the invariant η (G) as the maximum size of a clique disjoint edge set in G …

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some
classes of graphs. We compute the depth of the binomial edge ideal of a generalized block …

We prove that the regularity of binomial edge ideals of graphs obtained by gluing two graphs
at a free vertex is the sum of the regularity of individual graphs. As a consequence, we …

Let JG be the binomial edge ideal of a graph G. We characterize all graphs whose binomial
edge ideals, as well as their initial ideals, have regularity 3. Consequently we characterize …

In this paper we prove the conjectured upper bound for Castelnuovo–Mumford regularity of
binomial edge ideals posed in 23, in the case of chordal graphs. Indeed, we show that the …

We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of
block graphs by computing the two distinguished extremal Betti numbers of a new family of …