Results 41 to 50 of about 1,836,425 (146)

The Universal Gröbner Basis of a Binomial Edge Ideal

The Electronic Journal of Combinatorics, 2017
We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.
Mourtadha Badiane, Isaac Burke, Emil Sköldberg   +2 more
openaire   +4 more sources

On Binomial Edge Ideals of Corona of Graphs

Mediterranean Journal of Mathematics
For a simple graph $G$, let $J_G$ denote the corresponding binomial edge ideal. This article considers the binomial edge ideal of the corona product of two connected graphs $G$ and $H$. The corona product of $G$ and $H$, denoted by $G\circ H$, is a construction where each vertex of $G$ is connected (via the coning-off) to an entire copy of $H$. This is
Hajra, Buddhadev, Sarkar, Rajib
openaire   +2 more sources

F‐purity of binomial edge ideals

Journal of the London Mathematical Society
Abstract In 2012, Matsuda introduced the class of weakly closed graphs and investigated when binomial edge ideals are F‐pure. He proved that weakly closed binomial edge ideals are F‐pure whenever the base field has positive characteristic.
LaClair, Adam, McCullough, Jason
openaire   +2 more sources

$$(S_2)$$-condition and Cohen–Macaulay binomial edge ideals

Journal of Algebraic Combinatorics, 2022
AbstractWe describe the simplicial complex $$\Delta $$ Δ such that the initial ideal of the binomial edge ideal $$J_\textrm{G}$$ J G of G is the Stanley-Reisner ideal of $$\Delta $$ Δ .
Lerda, A, Mascia, C, Rinaldo, G, Romeo, F   +3 more
openaire   +3 more sources

Level and pseudo-Gorenstein binomial edge ideals

, 2023
We prove that level binomial edge ideals with regularity 2 and pseudo-Gorenstein binomial edge ideals with regularity 3 are cones, and we describe them completely. Also, we characterize level and pseudo-Gorenstein binomial edge ideals of bipartite graphs.
Rinaldo, Giancarlo, Rajib Sarkar, Giancarlo Rinaldo, Sarkar, Rajib   +3 more
core   +1 more source

Binomial edge ideals of Clutters

, 2021
In this paper, we introduce the notion of binomial edge ideals of a clutter and obtain results similar to those obtained for graphs by Rauf \& Rinaldo in \cite{raufrin}. We also answer a question posed in their paper.
Saha, Kamalesh, Sengupta, Indranath
openaire   +2 more sources

On the Depth of Generalized Binomial Edge Ideals

Mediterranean Journal of Mathematics
15 pages, 5 figures.
Anuvinda, J., Mehta, Ranjana, Saha, Kamalesh   +2 more
openaire   +3 more sources

On the Betti Numbers of some Classes of Binomial Edge Ideals [PDF]

The Electronic Journal of Combinatorics, 2013
We study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs depending on induced subgraphs.
Sohail Zafar, Zohaib Zahid
openaire   +4 more sources

Connected domination in graphs and v-numbers of binomial edge ideals [PDF]

, 2023
The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and originally motivated by problems in algebraic coding theory.
Jaramillo-Velez, Delio, Seccia, Lisa
core   +1 more source

Cohen-Macaulay Property of Binomial Edge Ideals with Girth of Graphs

Conca and Varbaro (Invent. Math. 221 (2020), no. 3) showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free.
Sengupta, Indranath, Saha, Kamalesh
core   +2 more sources