Complete intersection toric ideals of oriented graphs and chorded-theta subgraphs

  • Authors:

  • Isidoro Gitler;Enrique Reyes;Juan Antonio Vega

  • Affiliations:

  • Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN), México City, Mexico 07000;Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN), México City, Mexico 07000;Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN), México City, Mexico 07000

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let G=(V,E) be a finite, simple graph. We consider for each oriented graph $G_{\mathcal{O}}$ associated to an orientation ${\mathcal{O}}$ of the edges of G, the toric ideal $P_{G_{\mathcal{O}}}$ . In this paper we study those graphs with the property that $P_{G_{\mathcal{O}}}$ is a binomial complete intersection, for all ${\mathcal{O}}$ . These graphs are called $\text{CI}{\mathcal{O}}$ graphs. We prove that these graphs can be constructed recursively as clique-sums of cycles and/or complete graphs. We introduce chorded-theta subgraphs and some of their properties. Also we establish that the $\text{CI}{\mathcal{O}}$ graphs are determined by the property that each chorded-theta has a transversal triangle. Finally we explicitly give the minimal forbidden induced subgraphs that characterize these graphs, these families of forbidden graphs are: prisms, pyramids, thetas and a particular family of wheels that we call 驴-partial wheels.