{"paper":{"title":"Complete Intersection Toric Ideals of Oriented Graphs and Chorded-Theta Subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"E. Reyes, I. Gitler, J. A. Vega","submitted_at":"2012-12-27T20:59:50Z","abstract_excerpt":"Let $G=(V,E)$ be a finite, simple graph. We consider for each oriented graph $G_{\\cal O}$ associated to an orientation ${\\cal O}$ of the edges of $G$, the toric ideal $P_{G_{\\cal O}}$. In this paper we study those graphs with the property that $P_{G_{\\cal O}}$ is a binomial complete intersection, for all ${\\cal O}$. These graphs are called $\\text{CI}{\\cal O}$ graphs. We prove that these graphs can be constructed recursively as clique-sums of cycles and/or complete graphs. We introduce the chorded-theta subgraphs and their transversal triangles. Also we establish that the $\\text{CI}{\\cal O}$ gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6429","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}