The cut sets of a graph are special sets of vertices whose removal disconnects the graph.
They are fundamental in the study of binomial edge ideals, since they encode their minimal …

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 …

Let G be a graph on the vertex set [n] and JG the associated binomial edge ideal in the
polynomial ring S= K [x 1,…, xn, y 1,…, yn]. In this paper, we investigate the depth of …

Let $ G $ be a finite simple graph with $ n $ non isolated vertices, and let $ J_G $ its
binomial edge ideal. We determine all pairs $(\mbox {projdim}(J_G),\mbox {reg}(J_G)) …

Let G be a connected graph on the vertex set [n]. Then depth (S/JG)≤ n+ 1. In this paper, we
prove that if G is a unicyclic graph, then the depth of S/JG is bounded below by n. Also, we …

arXiv:2209.01201v3 [math.AC] 13 Jul 2023 Page 1 arXiv:2209.01201v3 [math.AC] 13 Jul 2023
RECENT RESULTS ON HOMOLOGICAL PROPERTIES OF BINOMIAL EDGE IDEAL OF …

Let $ G $ be a connected and simple graph on the vertex set $[n] $. To the graph $ G $ one
can associate the generalized binomial edge ideal $ J_ {m}(G) $ in the polynomial ring $ R …

Let $ G $ be a graph on the vertex set $[n] $ and $ J_G $ the associated binomial edge ideal
in the polynomial ring $ S=\mathbb {K}[x_1,\ldots, x_n, y_1,\ldots, y_n] $. In this paper we …

Let $ G $ be a simple connected non-complete graph on $ n $ vertices and $ J_G $ be its
binomial edge ideal. It is known that $ f (G)+ d (G)\leq depth (S/J_G)\leq n+ 2-\kappa (G) …

We calculate the local cohomology modules of the binomial edge ideals of the complements
of connected graphs of girth at least 5 using the poset and tools introduced by\Alvarez …