{"paper":{"title":"Extremal results for Berge-hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cory Palmer, D\\'aniel Gerbner","submitted_at":"2015-05-29T18:02:08Z","abstract_excerpt":"Let $G$ be a graph and $\\mathcal{H}$ be a hypergraph both on the same vertex set. We say that a hypergraph $\\mathcal{H}$ is a \\emph{Berge}-$G$ if there is a bijection $f : E(G) \\rightarrow E(\\mathcal{H})$ such that for $e \\in E(G)$ we have $e \\subset f(e)$. This generalizes the established definitions of \"Berge path\" and \"Berge cycle\" to general graphs. For a fixed graph $G$ we examine the maximum possible size (i.e.\\ the sum of the cardinality of each edge) of a hypergraph with no Berge-$G$ as a subhypergraph. In the present paper we prove general bounds for this maximum when $G$ is an arbitr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08127","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"}