Matching Stability for 3‐Partite 3‐Uniform Hypergraphs
ABSTRACT Let be three integers such that and . Let be a ‐partite ‐uniform hypergraph with vertices in each class. Aharoni (2017) showed that if , then has a matching of size . In this paper, we give a stability result for 3‐partite 3‐uniform hypergraphs: if is a 3‐partite 3‐uniform hypergraph with vertices in each class, and contains no matching of size , then has a vertex cover of size . Our bound is also tight.
Authors
- Hong-Liang Lü (ORCID: https://orcid.org/0000-0003-2398-720X)
- Xinxin Ma (ORCID: https://orcid.org/0000-0001-7616-1941)
Institutions
- Xi'an Jiaotong University (CN)
Publication Details
- Journal
- Journal of Graph Theory
- Published
- 2026-06-19
- DOI
- https://doi.org/10.1002/jgt.70089
- Primary Topic
- Cooperative Communication and Network Coding
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- National Key Research and Development Program of China