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Complete intersection toric ideals of oriented graphs and chorded-theta subgraphs
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gitler, Isidoro Reyes, Enrique Vega, Julio Acosta |
| Copyright Year | 2012 |
| 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 θ-partial wheels. |
| Starting Page | 721 |
| Ending Page | 744 |
| Page Count | 24 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10801-012-0421-x |
| Volume Number | 38 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1212.6429v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10801-012-0421-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
