{"paper":{"title":"On applications of Razborov's flag algebra calculus to extremal 3-graph theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emil R. Vaughan, Victor Falgas-Ravry","submitted_at":"2011-10-07T19:56:43Z","abstract_excerpt":"In this paper, we prove several new Tur\\'an density results for 3-graphs with independent neighbourhoods. We show:\n  \\pi(K_4^-, C_5, F_{3,2})=12/49, \\pi(K_4^-, F_{3,2})=5/18, and\n  \\pi(J_4, F_{3,2})=\\pi(J_5, F_{3,2})=3/8, where J_t is the 3-graph consisting of a single vertex x together with a disjoint set A of size t and all $\\binom{|A|}{2}$ 3-edges containing x.\n  We also prove two Tur\\'an density results where we forbid certain induced subgraphs:\n  \\pi(F_{3,2}, induced K_4^-)=3/8 and\n  \\pi(K_5, 5-set spanning 8 edges)=3/4.\n  The latter result is an analogue for K_5 of Razborov's result that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1623","kind":"arxiv","version":2},"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"}