Cohen-Macaulay binomial edge ideals of small graphs

被引：2

作者：

Bolognini, Davide ^{[1
]}

Macchia, Antonio ^{[1
,2
]}

Rinaldo, Giancarlo ^{[1
,3
]}

Strazzanti, Francesco ^{[1
,4
]}

机构：

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matematiche, Via Brecce Bianche, I-60131 Ancona, Italy

[2] Free Univ Berlin, Fachbereich Math & Informat, Arnimallee 2, D-14195 Berlin, Germany

[3] Univ Messina, Dipartimento Matemat & Informat Fis & Sci Terra, Viale Ferdinando Stagno Alcontres 31, I-98166 Messina, Italy

[4] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy

来源：

JOURNAL OF ALGEBRA | 2024年 / 638卷

关键词：

Binomial edge ideals; Cohen-Macaulay rings; Accessible set systems; Blocks with whiskers;

D O I：

10.1016/j.jalgebra.2023.09.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A combinatorial property that characterizes Cohen-Macaulay binomial edge ideals has long been elusive. A recent conjecture ties the Cohen-Macaulayness of a binomial edge ideal JG to special disconnecting sets of vertices of its underlying graph G, called cut sets. More precisely, the conjecture states that JG is Cohen-Macaulay if and only if JG is unmixed and the collection of the cut sets of G is an accessible set system. In this paper we prove the conjecture theoretically for all graphs with up to 12 vertices and develop an algorithm that allows to computationally check the conjecture for all graphs with up to 15 vertices and all blocks with whiskers where the block has at most 11 vertices. This significantly extends previous computational results.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

引用

页码：189 / 213

页数：25

共 20 条

[1] Local cohomology of binomial edge ideals and their generic initial ideals [J].