PROPERTIES OF CUT IDEALS ASSOCIATED TO RING GRAPHS

被引：23

作者：

Nagel, Uwe ^{[1
]}

Petrovic, Sonja ^{[2
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2009年 / 1卷 / 03期

关键词：

TORIC IDEALS; INVARIANTS;

D O I：

10.1216/JCA-2009-1-3-547

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A cut ideal of a graph records the relations among the cuts of the graph. These toric ideals have been introduced by Sturmfels and Sullivant who also posed the problem of relating their properties to the combinatorial structure of the graph. We study the cut ideals of the family of ring graphs, which includes trees and cycles. We show that they have quadratic Grobner bases and that their coordinate rings are Koszul, Hilbertian, and Cohen-Macaulay, but not Gorenstein in general.

引用

页码：547 / 565

页数：19

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