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arXiv · 0806.0585

Properties of cut ideals associated to ring graphs

Uwe Nagel·Sonja Petrović
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Abstract

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 Gröbner bases and that their coordinate rings are Koszul, Hilbertian, and Cohen-Macaulay, but not Gorenstein in general.

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Uwe Nagel, Sonja Petrović. 2009-04-28. Properties of cut ideals associated to ring graphs. https://arxiv.org/abs/0806.0585

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