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.

引用

页码：754 / 764

页数：11

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