{"paper":{"title":"Hypergraph Tur\\'an numbers of vertex disjoint cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li, Yongtang Shi","submitted_at":"2013-05-23T10:43:41Z","abstract_excerpt":"The Tur\\'an number of a $k$-uniform hypergraph $H$, denoted by $e{x_k}\\left({n;H} \\right)$, is the maximum number of edges in any $k$-uniform hypergraph $F$ on $n$ vertices which does not contain $H$ as a subgraph. Let $\\mathcal{C}_{\\ell}^{\\left(k \\right)}$ denote the family of all $k$-uniform minimal cycles of length $\\ell$, $\\mathcal{S}(\\ell_1,\\ldots,\\ell_r)$ denote the family of hypergraphs consisting of unions of $r$ vertex disjoint minimal cycles of length $\\ell_1,\\ldots,\\ell_r$, respectively, and $\\mathbb{C}_{\\ell}^{\\left(k \\right)}$ denote a $k$-uniform linear cycle of length $\\ell$. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5372","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"}