{"paper":{"title":"The Tur\\'an number of Berge-K_4 in triple systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andras Gyarfas","submitted_at":"2018-07-30T07:45:26Z","abstract_excerpt":"A Berge-$K_4$ in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\\{e_{ij}: 1\\le i< j \\le 4\\}$ such that $\\{v_i,v_j\\}\\subset e_{ij}$ for every $1\\le i<j\\le 4$. We denote by $\\cal{B}$ the set of Berge-$K_4$ configurations. A triple system is $\\cal{B}$-free if it does not contain any member of $\\cal{B}$. We prove that the maximum number of triples in a $\\cal{B}$-free triple system on $n\\ge 6$ points is obtained by the balanced complete $3$-partite triple system: all triples $\\{abc: a\\in A, b\\in B, c\\in C\\}$ where $A,B,C$ is a partition of $n$ poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11211","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"}