{"paper":{"title":"An exact Tur\\'an result for tripartite 3-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adam Sanitt, John Talbot","submitted_at":"2015-04-29T10:23:23Z","abstract_excerpt":"Mantel's theorem says that among all triangle-free graphs of a given order the balanced complete bipartite graph is the unique graph of maximum size. We prove an analogue of this result for 3-graphs. Let $K_4^-=\\{123,124,134\\}$, $F_6=\\{123,124,345,156\\}$ and $\\mathcal{F}=\\{K_4^-,F_6\\}$: for $n\\neq 5$ the unique $\\mathcal{F}$-free 3-graph of order $n$ and maximum size is the balanced complete tripartite 3-graph $S_3(n)$ (for $n=5$ it is $C_5^{(3)}=\\{123,234,345,145,125\\}$). This extends an old result of Bollob\\'as that $S_3(n) $ is the unique 3-graph of maximum size with no copy of $K_4^-=\\{123"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07796","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"}