{"paper":{"title":"Linear Turan numbers of r-uniform linear cycles and related Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Clayton Collier-Cartaino, Nathan Graber, Tao Jiang","submitted_at":"2014-04-20T05:41:23Z","abstract_excerpt":"An $r$-uniform hypergraph is called an $r$-graph. A hypergraph is linear if every two edges intersect in at most one vertex. Given a linear $r$-graph $H$ and a positive integer $n$, the linear Tur\\'an number $ex_L(n,H)$ is the maximum number of edges in a linear $r$-graph $G$ that does not contain $H$ as a subgraph. For each $\\ell\\geq 3$, let $C^r_\\ell$ denote the $r$-uniform linear cycle of length $\\ell$, which is an $r$-graph with edges $e_1,\\ldots, e_\\ell$ such that $\\forall i\\in [\\ell-1]$, $|e_i\\cap e_{i+1}|=1$, $|e_\\ell\\cap e_1|=1$ and $e_i\\cap e_j=\\emptyset$ for all other pairs $\\{i,j\\},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5015","kind":"arxiv","version":2},"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"}