TY - JOUR
T1 - Properties Of Cut Ideals Associated To Ring Graphs
AU - Nagel, Uwe
AU - PetroviĆ, Sonja
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/73649132342
UR - https://www.scopus.com/inward/citedby.url?scp=73649132342&partnerID=8YFLogxK
U2 - 10.1216/JCA-2009-1-3-547
DO - 10.1216/JCA-2009-1-3-547
M3 - Article
AN - SCOPUS:73649132342
SN - 1939-0807
VL - 1
SP - 547
EP - 565
JO - Journal of Commutative Algebra
JF - Journal of Commutative Algebra
IS - 3
ER -