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PreprintarXiv licencearXiv

Perfect Matching in k-Partite k-Uniform Hypergraphs

  • Jie Han
  • Hongliang Lu
  • Bin Wang
  • Feihong Yuan
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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≥5 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.

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Cite

BibTeXRIS
BibTeX
@misc{han2026perfect,
  title = {{Perfect Matching in $k$-Partite $k$-Uniform Hypergraphs}},
  author = {Jie Han and Hongliang Lu and Bin Wang and Feihong Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37290},
  eprint = {2609.37290},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37290},
}
RIS
TY  - UNPB
TI  - Perfect Matching in k-Partite k-Uniform Hypergraphs
AU  - Jie Han
AU  - Hongliang Lu
AU  - Bin Wang
AU  - Feihong Yuan
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37290
UR  - https://arxiv.org/abs/2609.37290
AB  - 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≥5 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.
ER  -