The invariant v-number was introduced very recently in the study of Reed-Muller-type codes.
Jaramillo and Villarreal (J. Combin. Theory Ser. A 177: 105310,) initiated the study of the v …

The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and
originally motivated by problems in algebraic coding theory. In this paper we study the case …

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 …

For a graph $ G $, Bolognini et al. have shown $ J_ {G} $ is strongly unmixed $\Rightarrow
$$ J_ {G} $ is Cohen-Macaulay $\Rightarrow $$ G $ is accessible, where $ J_ {G} $ denotes …

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 …

We determine the Castelnuovo-Mumford regularity of binomial edge ideals of complement
reducible graphs (cographs). For cographs with $ n $ vertices the maximum regularity grows …

Since the introduction of binomial edge ideals $ J_ {G} $ by Herzog et al. and independently
Ohtani, there has been significant interest in relating algebraic invariants of the binomial …

In this paper, I compute the regularity of the Rees algebra of binomial edge ideals of closed
graphs. I obtain a lower bound for the regularity of the Rees algebra of binomial edge ideals …

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 …