Title

Toric Geometry Of Series-Parallel Graphs

Keywords

Cycles; Edge-cuts; Generators; Kernel; Outerplanar graphs; Polynomial ring

Abstract

Let G be a graph and K be a field. We associate to G a projective toric variety Xq over K, the cut variety of the graph G.The cut ideal IG 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. © 2009 Society for Industrial and Applied Mathematics.

Publication Date

12-1-2009

Publication Title

SIAM Journal on Discrete Mathematics

Volume

23

Issue

2

Number of Pages

754-764

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/070703247

Socpus ID

73349116154 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/73349116154

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