Fractional and integer matchings in uniform hypergraphs

Abstract

Our main result improves bounds of Markstrom and Rucinski on the minimum d-degree which forces a perfect matching in a k-uniform hypergraph on n vertices. We also extend bounds of Bollobas, 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.

Accepted for publication by the European Journal of Combinatorics

References in corpus (3)

• The Clique Density Theorem
• On Erdos' extremal problem on matchings in hypergraphs
• Polynomial-time perfect matchings in dense hypergraphs

Cited by in corpus (7)

• Near Perfect Matchings in $k$-uniform Hypergraphs II
• Perfect Packings in Quasirandom Hypergraphs II
• The complexity of perfect matchings and packings in dense hypergraphs
• Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs
• Vertex degree sums for perfect matchings in 3-uniform hypergraphs
• Matching of given sizes in hypergraphs
• Improved Bound on Vertex Degree Version of Erdős Matching Conjecture