Depth of edge rings arising from finite graphs

2010/09/08 by Takayuki Hibi, Hibi, Takayuki, Akihiro Higashitani +5
Computer Science · Mathematics · #13P10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1009.1472

openalex publication_date 2010/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite graph and K[G] the edge ring of G. Based on the technique of Gröbner bases and initial ideals, it will be proved that, given integers f and d with 7 ≤ f ≤ d, there exists a finite graph G on [d]=1,...,d with \depth K[G] = f and with \Krull-dim K[G] = d.

Related

• Depth of initial ideals of normal edge rings
• Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity
• Behaviors of pairs of dimensions and depths of edge ideals
• Depth and Singular Varieties of Exterior Edge Ideals
• Depth, Stanley depth and regularity of ideals associated to graphs