Properties of cut ideals associated to ring graphs. (English) Zbl 1190.13016
To any finite simple graph \(G\) one can associate a homogeneous toric ideal \(I_{G}\) whose generators record relations among the cuts of \(G\). The ideal \(I_{G}\) is commonly known as the cut ideal of \(G\). In the paper under review the authors study the cut ideals of the family of ring graphs, which includes trees and cycles. They show that the cut ideal of a ring graph admits a squarefree quadratic Gröbner basis and that its coordinate ring is Koszul, Hilbertian, and Cohen-Macaulay, but not Gorenstein in general.
Reviewer: Anargyros Katsabekis (Lamia)
MSC:
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
Software:
4ti2References:
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