Related papers: Regularity bounds for binomial edge ideals

Assume that $G$ is a graph with edge ideal $I(G)$ and matching number ${\rm match}(G)$. For every integer $s\geq 1$, we denote the $s$-th squarefree power of $I(G)$ by $I(G)^{[s]}$. It is shown that for every positive integer $s\leq {\rm…

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…

Let $G$ be a simple undirected graph. The regular number of $G$ is defined to be the minimum number of subsets into which the edge set of $G$ can be partitioned so that the subgraph induced by each subset is regular. In this work, we obtain…

Let I = p_1^{m_1} \cap ... \cap p_s^{m_s} be the defining ideal of a scheme of fat points in P^{n_1} x ... x P^{n_k} with support in generic position. When all the m_i's are 1, we explicitly calculate the Castelnuovo-Mumford regularity of…

Let $G=C_{n}(S)$ be a circulant graph on $n$ vertices. In this paper we characterize chordal circulant graphs and then we compute $\nu (G)$, the induced matching number of $G$. These latter are useful in bounding the Castelnuovo-Mumford…

Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we prove that if $G$ is a fan graph of a complete graph, then…

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is the graph…

Let $R$ be a standard graded algebra over a field $k$. We prove an Auslander-Buchsbaum formula for the absolute Castelnuovo-Mumford regularity, extending important cases of previous works of Chardin and R\"omer. For a bounded complex of…

We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover, we introduce a new switching of graphs which does not change some algebraic invariants of graphs, and using this, we study the linear strand of the…

We consider the closed neighborhood ideal of square of the path graph and study some of its algebraic and homological invariants. We compute the height, the projective dimension and the Castelnuovo-Mumford regularity. We prove that these…

We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.

In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of…

We present algorithms for the computation of the Castelnuovo-Mumford regularity of the Rees algebra and of the fiber ring of equigenerated $\mm$-primary ideals in two variables. Applying these algorithms, we find a counter-example to a…

Let $\mathrm{rex}(n, F)$ denote the maximum number of edges in an $n$-vertex graph that is regular and does not contain $F$ as a subgraph. We give lower bounds on $\mathrm{rex}(n, F)$, that are best possible up to a constant factor, when…

We prove that for every integer $k\geq 1$, there exists a connected graph $H_k$ such that $v(H_k)=reg(H_k)+k$, where $v(G)$ and $reg(G)$ denote the $v$-number and the (Castelnuovo-Mumford) regularity of a graph $G$ respectively.

The regularity of an edge ideal of a finite simple graph $G$ is at least the induced matching number of $G$ and is at most the minimum matching number of $G$. If $G$ possesses a dominating inuduced matching, i.e., an induced matching which…

We first characterise graphs with binomial edge ideals of K\"onig type as those for which the path covering number is equal to a minor variant of the scattering number. These are well-studied graph-theoretic invariants, allowing us to apply…

In this article, we explore the class of graphs for which the projective dimension of the quotient of the binomial edge ideals matches the big height of that ideal. Additionally, we investigate the Vasconcelos number of binomial edge ideals…

In this paper, we obtain a combinatorial formula for computing the Betti numbers in the linear strand of edge ideals of bipartite Kneser graphs. We deduce lower and upper bounds for regularity of powers of edge ideals of these graphs in…

Let $G$ be a finite simple graph and let $I(G)$ denote its edge ideal. For $q \ge 1$, the $q$-th squarefree power $I(G)^{[q]}$ is generated by squarefree monomials corresponding to matchings of size $q$ in $G$. We denote by…