We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number â™¯V (G) of the vertices. We give Cohen-Macaulay criteria for such graphs.

Let K be a field, S = K[x1, . . . ,xn] be the polynomial ring in n variables with coefficient in K and M be a finitely generated Zn-graded S-module. Let u âˆˆM be a homogeneous element in M and Z aâ€¦ (More)

Let G be a connected simple graph. We prove that G is a closed graph if and only if G is a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graphâ€¦ (More)

We prove that a binomial edge ideal of a graph G has a quadratic GrÃ¶bner basis with respect to some term order if and only if the graph G is closed with respect to a given labelling of the vertices.â€¦ (More)

We present an application of Hilbert quasi-polynomials to order domain codes, allowing the effective computation of the order domain condition in a direct way. We also provide an improved andâ€¦ (More)

In recent years certification authorities (CAs) have been the target of multiple attacks due to their sensitive role in internet security. In fact, with access to malicious certificates it isâ€¦ (More)

We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type.â€¦ (More)

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.