{"paper":{"title":"On $r$-uniform linear hypergraphs with no Berge-$K_{2,t}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons","submitted_at":"2016-09-12T13:51:17Z","abstract_excerpt":"Let $\\mathcal{F}$ be an $r$-uniform hypergraph and $G$ be a multigraph. The hypergraph $\\mathcal{F}$ is a Berge-$G$ if there is a bijection $f: E(G) \\rightarrow E( \\mathcal{F} )$ such that $e \\subseteq f(e)$ for each $e \\in E(G)$. Given a family of multigraphs $\\mathcal{G}$, a hypergraph $\\mathcal{H}$ is said to be $\\mathcal{G}$-free if for each $G \\in \\mathcal{G}$, $\\mathcal{H}$ does not contain a subhypergraph that is isomorphic to a Berge-$G$. We prove bounds on the maximum number of edges in an $r$-uniform linear hypergraph that is $K_{2,t}$-free. We also determine an asymptotic formula fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03401","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"}