{"paper":{"title":"New Tur\\'an densities for 3-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Talbot, Rahil Baber","submitted_at":"2011-10-19T13:58:53Z","abstract_excerpt":"If $\\mathcal{F}$ is a family of graphs then the Tur\\'an density of $\\mathcal{F}$ is determined by the minimum chromatic number of the members of $\\mathcal{F}$.\n  The situation for Tur\\'an densities of 3-graphs is far more complex and still very unclear. Our aim in this paper is to present new exact Tur\\'an densities for individual and finite families of 3-graphs, in many cases we are also able to give corresponding stability results. As well as providing new examples of individual 3-graphs with Tur\\'an densities equal to 2/9,4/9,5/9 and 3/4 we also give examples of irrational Tur\\'an densities"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4287","kind":"arxiv","version":3},"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"}