Our main result improves bounds of Markström and Ruciński on the minimum d-degree which forces a perfect matching in a k-uniform hypergraph on n vertices. We also extend bounds of Bollobás, Daykin and Erdos by asymptotically determining the minimum vertex degree which forces a matching of size t < n / 2 (k - 1) in a k-uniform hypergraph on n vertices. Further asymptotically tight results on d-degrees which force large matchings are also obtained. Our approach is to prove fractional versions of the above results and then translate these into integer versions.
ASJC Scopus subject areas
- Geometry and Topology
- Theoretical Computer Science
- Computational Theory and Mathematics