{"paper":{"title":"Almost perfect matchings in $k$-partite $k$-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Xingxing Yu, Yan Wang","submitted_at":"2016-08-17T02:37:11Z","abstract_excerpt":"The minimum co-degree threshold for a perfect matching in a $k$-graph with $n$ vertices was determined by R\\\"odl, Ruci\\'nski and Szemer\\'edi for the case when $n\\equiv 0\\pmod k$. Recently, Han resolved the remaining cases when $n \\not\\equiv 0\\pmod k$, establishing a conjecture of R\\\"odl, Ruci\\'nski and Szemer\\'edi. In this paper, we determine the minimum co-degree threshold for almost perfect matchings in $k$-partite $k$-graphs, answering a question of R\\\"odl and Ruci\\'nski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04838","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"}