{"paper":{"title":"Asymptotics for the Tur\\'an number of Berge-$K_{2,t}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, D\\'aniel Gerbner, M\\'at\\'e Vizer","submitted_at":"2017-05-11T12:30:51Z","abstract_excerpt":"Let $F$ be a graph. A hypergraph is called Berge-$F$ if it can be obtained by replacing each edge of $F$ by a hyperedge containing it. Let $\\mathcal{F}$ be a family of graphs. The Tur\\'an number of Berge-$\\mathcal{F}$ is the maximum possible number of edges in an $r$-uniform hypergraph on $n$ vertices containing no Berge-$F$ as a subhypergraph (for every $F \\in \\mathcal{F}$) and is denoted by $ex_r(n,\\mathcal{F})$.\n  We determine the asymptotics for the Tur\\'an number of Berge-$K_{2,t}$ by showing $$ex_3(n,K_{2,t})=\\frac{1}{6}(t-1)^{3/2} \\cdot n^{3/2}(1+o(1))$$ for any given $t \\ge 7$. We stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04134","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"}