{"paper":{"title":"Minimum co-degree condition for 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":"2017-11-22T09:16:04Z","abstract_excerpt":"Let $H$ be a $k$-partite $k$-graph with $n$ vertices in each partition class, and let $\\delta_{k-1}(H)$ denote the minimum co-degree of $H$. We characterize those $H$ with $\\delta_{k-1}(H) \\geq n/2$ and with no perfect matching. As a consequence we give an affirmative answer to the following question of R\\\"odl and Ruci\\'nski: If $k$ is even or $n \\not\\equiv 2 \\pmod 4$, does $\\delta_{k-1}(H) \\geq n/2$ imply that $H$ has a perfect matching? We also give an example indicating that it is not sufficient to impose this degree bound on only two types of $(k-1)$-sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08185","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"}