{
  "abstract": "A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph whose vertex set is partitioned into $k$ classes of the same size and whose edges meet every class in exactly one vertex. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings when $k=3$, and Lu, Wang and Yuan recently determined it when $k=4$. We prove the corresponding exact result for every fixed $k\\ge5$ and all sufficiently large class sizes. The close case follows from the general theorem of Lu, Wang and Yuan. For the non-closed case, we extend their stability result from the 3-partite setting to arbitrary partite uniformity, using the probability-tail rigidity theorem of Cao, Liu and Zhang, thereby replacing the earlier weighted lemma.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37290",
  "author_total": 4,
  "authors": [
    {
      "name": "Jie Han"
    },
    {
      "name": "Hongliang Lu"
    },
    {
      "name": "Bin Wang"
    },
    {
      "name": "Feihong Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbtm37c4pnhjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37290",
  "fulltext_url": null,
  "id": "cbtm37c4pnhjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37290",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.37290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbtm37c4pnhjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37290"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Perfect Matching in $k$-Partite $k$-Uniform Hypergraphs",
  "title_text": "Perfect Matching in k-Partite k-Uniform Hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/cbtm37c4pnhjw",
  "venue": "arXiv",
  "versions": []
}