Almost complete intersection binomial edge ideals and their Rees algebras

2019/04/09 by A. V. Jayanthan, Arvind Kumar, Jayanthan, A. V. +3
Computer Science · Mathematics · Medicine · #05E40 #13C13 #13D02 #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1904.04499

openalex publication_date 2019/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simple graph on n vertices and J_G denote the binomial edge ideal of G in the polynomial ring S = \mathbbK[x₁, …, x_n, y₁, …, y_n]. In this article, we compute the second graded Betti numbers of J_G, and we obtain a minimal presentation of it when G is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a d-sequence and that the Rees algebra of their binomial edge ideal is Cohen-Macaulay. We also obtain an explicit description of the defining ideal of the Rees algebra of those binomial edge ideals.

Related

• Cohen-Macaulay generalized binomial edge ideals
• On the v-number of binomial edge ideals of some classes of graphs
• Extremal Betti numbers of some classes of binomial edge ideals
• Rees algebra and special fiber ring of binomial edge ideals of closed graphs
• On the binomial edge ideals of proper interval graphs