Abstract
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.
Original language | English |
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Pages (from-to) | 83-96 |
Number of pages | 14 |
Journal | European Journal of Combinatorics |
Volume | 38 |
DOIs | |
Publication status | Published - 1 May 2014 |
ASJC Scopus subject areas
- Geometry and Topology
- Theoretical Computer Science
- Computational Theory and Mathematics