Properties of cut ideals associated to ring graphs

Details Properties of cut ideals associated to ring graphs Properties of cut ideals associated to ring graphs

2008-06-03

arxiv.org/abs/0806.0585v3

Mathematics

Commutative Algebra

References corrected/updated. 11 pages. To appear in the Journal of Commutative Algebra

Scientific paper

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 Gr\"obner bases and that their coordinate rings are Koszul, Hilbertian, and Cohen-Macaulay, but not Gorenstein in general.

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