Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is
the ideal generated by the binomials xiyj− xj yi, 1≤ i< j≤ n, in the polynomial ring S= K …

Let $ G $ be a simple graph on $ n $ vertices. We introduce the notion of bipartite
connectivity of $ G $, denoted by $\operatorname {bc}(G) $ and prove that $$\lim_ {s\to\infty} …

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 …

Let G be a graph and let I:= I (G) be its edge ideal. In this paper, we provide an upper bound
of n from which depth R/I (G) n is stationary, and compute this limit explicitly. This bound is …

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Let G be a simple graph on n vertices and J_G JG denote the corresponding binomial edge
ideal in S= K x_1, ..., x_n, y_1, ..., y_n. S= K x 1,…, xn, y 1,…, yn. We prove that the …

A very well-covered graph is a well-covered graph without isolated vertices such that the
size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay …

Let I= I (D) be the edge ideal of a weighted oriented graph D. We determine the irredundant
irreducible decomposition of I. Also, we characterize the associated primes and the unmixed …

Binomial edge ideals IG of a graph G were introduced by [4]. They found some classes of
graphs G with the property that IG is a Cohen-Macaulay ideal. This might happen only for …

We characterize all pairs of graphs $(G_1, G_2) $, for which the binomial edge ideal $ J_
{G_1, G_2} $ has linear relations. We show that $ J_ {G_1, G_2} $ has a linear resolution if …