Matchings in 3-uniform hypergraphs of large minimum vertex degree
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Colleges, School and Institutes
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.
|Number of pages||6|
|Journal||Electronic Notes in Discrete Mathematics|
|Publication status||Published - 1 Dec 2011|