{"paper":{"title":"On tight cycles in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Huang, Jie Ma","submitted_at":"2017-11-20T17:57:46Z","abstract_excerpt":"A tight $k$-uniform $\\ell$-cycle, denoted by $TC_\\ell^k$, is a $k$-uniform hypergraph whose vertex set is $v_0, \\cdots, v_{\\ell-1}$, and the edges are all the $k$-tuples $\\{v_i, v_{i+1}, \\cdots, v_{i+k-1}\\}$, with subscripts modulo $\\ell$. Motivated by a classic result in graph theory that every $n$-vertex cycle-free graph has at most $n-1$ edges, S\\'os and, independently, Verstra\\\"ete asked whether for every integer $k$, a $k$-uniform $n$-vertex hypergraph without any tight $k$-uniform cycles has at most $\\binom{n-1}{k-1}$ edges. In this paper, we answer this question in negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07442","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"}