TORIC GEOMETRY OF SERIES-PARALLEL GRAPHS

被引：2
|
作者：
Brennan, Joseph [1 ]
Chen, Guantao [2 ]
机构：
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 2009年 / 23卷 / 02期
关键词：
cycles; outerplanar graphs; edge-cuts; polynomial ring; kernel; generators;
D O I：
10.1137/070703247
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a graph and K be a field. We associate to G a projective toric variety X-G over K, the cut variety of the graph G. The cut ideal I-G of the graph G is the ideal defining the cut variety. We show that, if G is a subgraph of a subdivision of a book or an outerplanar graph, then the minimal generators are quadrics. Furthermore, we describe the generators of the cut ideal of a subdivision of a book.
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页码：754 / 764
页数：11
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