{"paper":{"title":"A hypergraph Tur\\'an theorem via lagrangians of intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hefetz, Peter Keevash","submitted_at":"2013-07-31T18:53:10Z","abstract_excerpt":"Let $\\mc{K}_{3,3}^3$ be the 3-graph with 15 vertices $\\{x_i, y_i: 1 \\le i \\le 3\\}$ and $\\{z_{ij}: 1 \\le i,j \\le 3\\}$, and 11 edges $\\{x_1, x_2, x_3\\}$, $\\{y_1, y_2, y_3\\}$ and $\\{\\{x_i, y_j, z_{ij}\\}: 1 \\le i,j \\le 3\\}$. We show that for large $n$, the unique largest $\\mc{K}_{3,3}^3$-free 3-graph on $n$ vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof uses the stability method and a result on lagrangians of intersecting families that has independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8423","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"}