{"paper":{"title":"Codegree threshold for tiling $k$-graphs with two edges sharing exactly $\\ell$ vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lei Yu, Xinmin Hou","submitted_at":"2018-08-07T12:16:54Z","abstract_excerpt":"Given integer $k$ and a $k$-graph $F$, let $t_{k-1}(n,F)$ be the minimum integer $t$ such that every $k$-graph $H$ on $n$ vertices with codegree at least $t$ contains an $F$-factor. For integers $k\\geq3$ and $0\\leq\\ell\\leq k-1$, let $\\mathcal{Y}_{k,\\ell}$ be a $k$-graph with two edges that shares exactly $\\ell$ vertices. Han and Zhao (JCTA, 2015) asked the following question: For all $k\\ge 3$, $0\\le \\ell\\le k-1$ and sufficiently large $n$ divisible by $2k-\\ell$, determine the exact value of $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})$. In this paper, we show that $t_{k-1}(n,\\mathcal{Y}_{k,\\ell})=\\frac{n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02319","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"}