{"paper":{"title":"Matchings in $k$-partite $k$-uniform Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chuanyun Zang, Jie Han, Yi Zhao","submitted_at":"2016-11-01T16:42:06Z","abstract_excerpt":"For $k\\ge 3$ and $\\epsilon>0$, let $H$ be a $k$-partite $k$-graph with parts $V_1,\\dots, V_k$ each of size $n$, where $n$ is sufficiently large. Assume that for each $i\\in [k]$, every $(k-1)$-set in $\\prod_{j\\in [k]\\setminus \\{i\\}} V_i$ lies in at least $a_i$ edges, and $a_1\\ge a_2\\ge \\cdots \\ge a_k$. We show that if $a_1, a_2\\ge \\epsilon n$, then $H$ contains a matching of size $\\min\\{n-1, \\sum_{i\\in [k]}a_i\\}$. In particular, $H$ contains a matching of size $n-1$ if each crossing $(k-1)$-set lies in at least $\\lceil n/k \\rceil$ edges, or each crossing $(k-1)$-set lies in at least $\\lfloor n/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00290","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"}