Cohen-Macaulay binomial edge ideals

By Viviana Ene, Jürgen Herzog, Takayuki Hibi. Nagoya mathematical journal, 2010

146 citations recorded by the source corpus.

Abstract We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen-Macaulay.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/a6f8466d315390f899f21aefffee017d9393813f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Sohail Zafar
2. Dariush Kiani
3. Sara Saeedi Madani
4. Asia Rauf
5. Peter Schenzel
6. Giancarlo Rinaldo

In Computational Theory and Mathematics

1. Sohail Zafar
2. Sara Saeedi Madani
3. Dariush Kiani
4. Asia Rauf
5. Peter Schenzel
6. Giancarlo Rinaldo

In Pharmacology

1. Sara Saeedi Madani
2. Dariush Kiani
3. Sohail Zafar
4. Peter Schenzel

Citations in the corpus

• Some Cohen–Macaulay and Unmixed Binomial Edge Ideals (2015, background): “Hence, we generalize the result of [3] about block graphs.”
• Algebraic properties of the binomial edge ideal of a complete bipartite graph (2013, methodology): “e graph G one can associate an ideal JG ⊂ S generated by all binomials xiyj − xjyi for all 1 ≤ i < j ≤ n such that {i,j} is an edge of G. This construction was invented by Herzog et al. in [6] and [4]. At first let us recall some of their definitions. Definition 2.1. Fix the previous notation. For a”
• Construction of Cohen–Macaulay Binomial Edge Ideals (2012, background): “Algebraic properties of binomial edge ideals in terms of properties of the underlying graph were studied in [6], [2] and [7].”