{"paper":{"title":"Tiling multipartite hypergraphs in Quasi-random Hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Jie Han, Laihao Ding, Shumin Sun, Wenling Zhou","submitted_at":"2021-11-28T13:38:12Z","abstract_excerpt":"Given $k\\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an \\emph{$F$-factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi studied the $F$-factor problems in quasi-random $k$-graphs with minimum degree $\\Omega(n^{k-1})$. In particular, they constructed a sequence of $1/8$-dense quasi-random $3$-graphs $H(n)$ with minimum degree $\\Omega(n^2)$ and minimum codegree $\\Omega(n)$ but with no $K_{2,2,2}$-factor. We prove that if $p>1/8$ and $F$ is a $3$-partite $3$-graph with $f$ vertices, then for sufficiently large $n$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14140","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.14140/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}