Properties Of Cut Ideals Associated To Ring Graphs

Uwe Nagel, Sonja PetroviĆ

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


A cut ideal of a graph records the relations among the cuts of the graph. These toricideals 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 Goren-stein in general.

Original languageEnglish
Pages (from-to)547-565
Number of pages19
JournalJournal of Commutative Algebra
Issue number3
StatePublished - 2009

ASJC Scopus subject areas

  • Algebra and Number Theory


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