Fractional and integer matchings in uniform hypergraphs

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Colleges, School and Institutes


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 languageEnglish
Pages (from-to)83-96
Number of pages14
JournalEuropean Journal of Combinatorics
Publication statusPublished - 1 May 2014