Geodesic
Complete intersection toric ideals of oriented graphs and chorded-theta subgraphs
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 721-744.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 ${CI}{\mathcal{O}}$ 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 ${CI}{\mathcal{O}}$ 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 $\theta $-partial wheels.
Keywords: toric ideals, oriented graphs, complete intersections, forbidden induced subgraphs 
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     author = {Gitler, Isidoro and Reyes, Enrique and Vega, Juan Antonio},
     title = {Complete intersection toric ideals of oriented graphs and chorded-theta subgraphs},
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     pages = {721--744},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a1/}
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Gitler, Isidoro; Reyes, Enrique; Vega, Juan Antonio. Complete intersection toric ideals of oriented graphs and chorded-theta subgraphs. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 721-744. http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a1/