Related papers: Binomial edge ideals of Clutters
We discuss algebraic and homological properties of binomial edge ideals associated to graphs which are obtained by gluing of subgraphs and the formation of cones.
Let $G$ be a cycle or a complete bipartite graph. We show that the binomial edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic order have the same extremal Betti number.
We prove several cases of the Betti number conjecture for the binomial edge ideal $J_G$ of a proper interval graph $G$ (also known as closed graph). Namely, we show that this conjecture is true for the linear strand of $J_G$, and true in…
We give a combinatorial characterisation of connected graphs whose binomial edge ideals are of K\"{o}nig type, developed independently to the similar characterisation given by LaClair in arXiv:2304.13299, and exhibit some classes of graphs…
Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge…
We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in…
We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…
In this work, some combinatorial lower bound for regularity of powers of the edge ideal of a uniform hypergarph is gained. A family of hypergraphs whose regularity of edge ideal attains this bound and has a significant difference from the…
We give upper bounds for the Stanley depth of edge ideals of certain k-partite clutters. In particular, we generalize a result of Ishaq about the Stanley depth of the edge ideal of a complete bipartite graph. A result of Pournaki, Seyed…
It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs.
In this article, we compute the regularity of Rees algebra of binomial edge ideals of closed graphs. We obtain a lower bound for the regularity of Rees algebra of binomial edge ideals. We also study some algebraic properties of the Rees…
We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one extremal Betti number.
Let $J_G$ denote the binomial edge ideal of a connected undirected graph on $n$ vertices. This is the ideal generated by the binomials $x_iy_j - x_jy_i, 1\leq i < j \leq n,$ in the polynomial ring $S= K[x_1,...,x_n,y_1,...,y_n]$ where…
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…
We determine the arithmetical rank of every edge ideal of a Ferrers graph.
We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of…
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 few classes of graphs. A certain generalization of being…
Let C be a uniform clutter and let I=I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp.…
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 block graphs, called flower graphs. Moreover, we present a…
We prove a conjectured upper bound for the Castelnuovo-Mumford regularity of binomial edge ideals of graphs, due to Matsuda and Murai. Indeed, we prove that $\mathrm{reg}(J_G)\leq n-1$ for any graph $G$ with $n$ vertices, which is not a…