Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
A Dirac-Type Theorem for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Hamiltonian chains in hypergraphs
Journal of Graph Theory
Matchings in hypergraphs of large minimum degree
Journal of Graph Theory
Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
Journal of Combinatorial Theory Series B
Co-degree density of hypergraphs
Journal of Combinatorial Theory Series A
Perfect matchings in r-partite r-graphs
European Journal of Combinatorics
Perfect matchings in large uniform hypergraphs with large minimum collective degree
Journal of Combinatorial Theory Series A
Dirac-type results for loose Hamilton cycles in uniform hypergraphs
Journal of Combinatorial Theory Series B
Perfect matchings (and Hamilton cycles) in hypergraphs with large degrees
European Journal of Combinatorics
Large matchings in uniform hypergraphs and the conjectures of Erdős and Samuels
Journal of Combinatorial Theory Series A
Exact minimum degree thresholds for perfect matchings in uniform hypergraphs
Journal of Combinatorial Theory Series A
Matchings in 3-uniform hypergraphs
Journal of Combinatorial Theory Series B
Polynomial-time perfect matchings in dense hypergraphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Fractional and integer matchings in uniform hypergraphs
European Journal of Combinatorics
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A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a perfect matching in terms of a variant of the minimum degree. We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k - 1 vertices is contained in n/2 + Ω(log n) edges. Owing to a construction in [D. Kühn, D. Osthus, Matchings in hypergraphs of large minimum degree, J. Graph Theory 51 (1) (2006) 269-280], this is nearly optimal. For almost perfect and fractional perfect matchings we show that analogous thresholds are close to n/k rather than n/2.