Results 21 to 30 of about 1,836,425 (146)

Regularity of powers of binomial edge ideals of complete multipartite graphs

, 2023
summary:Let $G=K_{n_1,n_2,\ldots ,n_r}$ be a complete multipartite graph on $[n]$ with $n>r>1$ and $J_G$ being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity ${\rm reg}(J^t_G)$ is $2t+1$ for any positive integer $t$
Wang, Hong, Tang, Zhongming
core   +1 more source

Binomial edge ideals of regularity 3 [PDF]

Journal of Algebra, 2018
Let $J_G$ be the binomial edge ideal of a graph $G$. We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity $3$. Consequently we characterize all graphs $G$ such that $J_G$ is extremal Gorenstein. Indeed, these characterizations are consequences of an explicit formula we obtain for the regularity of the ...
Saeedi Madani, Sara, Kiani, Dariush
openaire   +2 more sources

On the Symbolic Powers of Binomial Edge Ideals [PDF]

, 2020
We show that under some conditions, if the initial ideal in ...
Ene, Viviana, Herzog, Jürgen
openaire   +2 more sources

A combinatorial characterization of $S_2$ binomial edge ideals

Eur. J. Comb., 2023
Several algebraic properties of a binomial edge ideal $J_G$ can be interpreted in terms of combinatorial properties of its associated graph $G$. In particular, the so-called cut sets of a graph $G$, special sets of vertices that disconnect $G$ in a minimal way, play an important role since they are in bijection with the minimal prime ideals of $J_G ...
Bolognini D., Macchia A., Rinaldo G., Strazzanti F.   +3 more
openaire   +4 more sources

Cohen-Macaulay binomial edge ideals [PDF]

Nagoya Mathematical Journal, 2011
Abstract We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen-Macaulay.
Ene, Viviana, Herzog, Jürgen, Hibi, Takayuki   +2 more
openaire   +4 more sources

d-Sequence edge binomials, and regularity of powers of binomial edge ideals of trees

Journal of Algebra and Its Applications, 2023
In this paper, we provide the necessary and sufficient conditions for the edge binomials of the tree forming a [Formula: see text]-sequence in terms of the degree sequence notion of a graph. We study the regularity of powers of the binomial edge ideals of trees generated by [Formula: see text]-sequence edge binomials.
Marie Amalore Nambi, Neeraj Kumar
openaire   +4 more sources

Waldschmidt constant of some classes of hypergraphs [PDF]

AUT Journal of Mathematics and Computing
In this paper, we present a formula for the Waldschmidt constant of edge ideals of some classes of hypergraphs. We also show that if $G$ is a simple graph with binomial edge ideal $J_G$, then the Waldschmidt constant of $J_G$ is always 2.
Iman Jahani, Shamila Bayati
doaj   +1 more source

Bayesian Verification Scheme for Software Reliability Based on Staged Growth Test Information [PDF]

Jisuanji kexue
The prior distribution determination methods of existing Bayesian schemes are relatively conservative and ideal for processing software reliability phased growth testing information.In this article,an edge distribution model for the software success ...
WANG Yuzhuo, LIU Haitao, YUAN Haojie, ZHAI Yali, ZHANG Zhihua
doaj   +1 more source

Binomial Edge Ideals with Quadratic Gröbner Bases [PDF]

The Electronic Journal of Combinatorics, 2011
We prove that a binomial edge ideal of a graph $G$ has a quadratic Gröbner 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. We also state some criteria for the closedness of a graph $G$ that do not depend on the labelling of its vertex set.
CRUPI, Marilena, RINALDO, GIANCARLO
openaire   +4 more sources

Algebraic properties of the binomial edge ideal of a complete bipartite graph

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj − xjyi, 1 ≤ i < j≤ n, in the polynomial ring S = K[x1, . . . , xn, y1, . . . , yn] where {i, j} is an edge of G.
Schenzel Peter, Zafar Sohail
doaj   +1 more source