DOI: 10.1002/jgt.70089 ISSN: 0364-9024
Matching Stability for 3‐Partite 3‐Uniform Hypergraphs
Hongliang Lu, Xinxin MaABSTRACT
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.