# Binomial edge ideals and conditional independence statements

@article{Herzog2010BinomialEI, title={Binomial edge ideals and conditional independence statements}, author={J{\"u}rgen Herzog and Takayuki Hibi and Freyja Hreinsd{\'o}ttir and Thomas Kahle and Johannes Rauh}, journal={Adv. Appl. Math.}, year={2010}, volume={45}, pages={317-333} }

## 179 Citations

Binomial Edge Ideals and Related Ideals

- Mathematics
- 2018

In this chapter we consider classes of binomial ideals which are naturally attached to finite simple graphs. The first of these classes are the binomial edge ideals. These ideals may also be viewed…

Cohen–Macaulay binomial edge ideals and accessible graphs

- MathematicsJournal of Algebraic Combinatorics
- 2021

The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary…

Combinatorial And Arithmetic Study Of Binomial Edge Ideal

- Mathematics
- 2008

Let JG denote the binomial edge ideal of a connected undirected graph G on n vertices.This is the ideal generated by the binomials xiyjxjyi; 1 i < j n; in the polynomial ring S = K[x1; : : : ; xn;…

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

- Mathematics
- 2013

Abstract 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,…

Almost complete intersection binomial edge ideals and their Rees algebras

- MathematicsJournal of Pure and Applied Algebra
- 2021

Some Computations for Binomial Edge Ideals and Koszul Duality

- Mathematics
- 2014

We make some observations on binomial edge ideals, with the characterization of their Koszulness as motivation. Inspired by results of Ene, Herzog and Hibi, we discuss building Koszul graphs from…

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