On the maximum number of edges in a hypergraph with a unique perfect matching

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On the maximum number of edges in a hypergraph with a unique perfect matching

In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a unique perfect matching. This settles a conjecture proposed by Snevily.

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On the maximum number of edges in a hypergraph with given matching number

The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max {(3s+ 2 3 ) , ( n 3 ) − ( n− s 3 )} for all n, s, n ≥ 3s+ 2.

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2011

ISSN: 0012-365X

DOI: 10.1016/j.disc.2011.07.016