Related papers: On the arithmetical rank of the edge ideals of for…

We show that for the edge ideals of the graphs consisting of one cycle or two cycles of any length connected through a vertex or a path, the arithmetical rank equals the projective dimension.

In this paper we provide some exact formulas for projective dimension and the regularity of powers of edge ideals of vertex-weighted rooted forests. These formulas are functions of the weight of the vertices and the number of edges. We also…

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In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. As some consequences, we give some exact formulas for the depth of…

We consider the edge ideals of large classes of graphs with whiskers and for these ideals we prove that the arithmetical rank is equal to the big height. Then we extend these results to other classes of squarefree monomial ideals, generated…

Let $I\subset S=K[x_1,...,x_n]$ be a lexsegment edge ideal or the Alexander dual of such an ideal. In both cases it turns out that the arithmetical rank of $I$ is equal to the projective dimension of $S/I.$

In this note, we classify all the weighted oriented forests whose edge ideals have the property that one of their matching powers has linear resolution.

We determine the arithmetical rank of every edge ideal of a Ferrers graph.

This paper gives exact formulas for the regularity of edge ideals of edge-weighted integrally closed trees. In addition, we provide some linear upper bounds on the regularity of powers of such ideals.

We give an affirmative answer to a question due to J. He and A. Van Tuyl, proving that the arithmetical rank of a special monomial ideal equals to the projective dimension of corresponding quotient module.

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.

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…

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.

Let $I(G)^{[k]}$ denote the $k$th squarefree power of the edge ideal of $G$. When $G$ is a forest, we provide a sharp upper bound for the regularity of $I(G)^{[k]}$ in terms of the $k$-admissable matching number of $G$. For any positive…

We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.

We describe all the trees with the property that the corresponding edge ideal of the square of the tree has a linear resolution. As a consequence, we give a complete characterization of those trees $T$ for which the square is co-chordal,…

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 $R=K[x_{ij}: i \in [m], j \in [n]]$. We provide a lower bound for the…

We prove that the regularity of edge ideals of powers of forests is weakly decreasing. We then compute the regularity of edge ideals of powers of cycles.

Let $R$ be a polynomial ring over a field $K$. To a given squarefree monomial ideal $I \subset R$, one can associate a hypergraph $H(I)$. In this article, we prove that the arithmetical rank of $I$ is equal to the projective dimension of…

We prove that the class of trees with unique minimum edge-vertex dominating sets is equivalent to the class of trees with unique minimum paired dominating sets.