The Regularity of Edge Rings and Matching Numbers

Author:

Herzog Jürgen,Hibi Takayuki

Abstract

Let K [ G ] denote the edge ring of a finite connected simple graph G on [ d ] and mat ( G ) the matching number of G. It is shown that reg ( K [ G ] ) ≤ mat ( G ) if G is non-bipartite and K [ G ] is normal, and that reg ( K [ G ] ) ≤ mat ( G ) − 1 if G is bipartite.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference6 articles.

1. Normal Polytopes Arising from Finite Graphs

2. Binomial Ideals;Herzog,2018

3. Matching numbers and the regularity of the Rees algebra of an edge ideal;Herzog;arXiv,2019

4. Monomial Algebras;Villarreal,2015

5. Degree bounds in monomial subrings

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Eulerian ideals;Communications in Algebra;2022-08-05

2. Rees algebra and special fiber ring of binomial edge ideals of closed graphs;Illinois Journal of Mathematics;2022-04-01

3. Properties of the Toric Rings of a Chordal Bipartite Family of Graphs;Association for Women in Mathematics Series;2021

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