{"paper":{"title":"Hypergraph Tur\\'an problem of the generalized triangle with bounded matching number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jian Wang, Weihua Yang, Wenbin Wang","submitted_at":"2025-07-06T23:51:05Z","abstract_excerpt":"Let $\\mathcal{H}$ be a 3-graph on $n$ vertices. The matching number $\\nu(\\mathcal{H})$ is defined as the maximum number of disjoint edges in $\\mathcal{H}$. The generalized triangle $F_5$ is a 3-graph on the vertex set $\\{a,b,c,d,e\\}$ with the edge set $\\{abc, abd,cde\\}$. In this paper, we showed that an $F_5$-free 3-graph $\\mathcal{H}$ with matching number at most $s$ has at most $s\\lfloor (n-s)^2/4\\rfloor$ edges for $n\\geq 30(s+1)$ and $s\\geq 3$. For the proof, we establish a 2-colored version of Mantel's theorem, which may be of independent interests."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04579","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04579/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}