{"paper":{"title":"Asymptotics for Tur\\'an numbers of cycles in 3-uniform linear hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Beka Ergemlidze, Ervin Gy\\H{o}ri","submitted_at":"2017-05-09T22:45:59Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of $3$-uniform linear hypergraphs. The linear Tur\\'an number of $\\mathcal F$ is the maximum possible number of edges in a $3$-uniform linear hypergraph on $n$ vertices which contains no member of $\\mathcal{F}$ as a subhypergraph.\n  In this paper we show that the linear Tur\\'an number of the five cycle $C_5$ (in the Berge sense) is $\\frac{1}{3 \\sqrt3}n^{3/2}$ asymptotically. We also show that the linear Tur\\'an number of the four cycle $C_4$ and $\\{C_3, C_4\\}$ are equal asmptotically, which is a strengthening of a theorem of Lazebnik and Verstra\\\"ete.\n  We establis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03561","kind":"arxiv","version":3},"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"}