We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than (n-12)-(2n/32), then H contains a perfect matching. This bound is tight and answers a question of Hàn, Person and Schacht. More generally, we determine the minimum vertex degree threshold that ensures that H contains a matching of size d≤n/3.
- Vertex degree
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics