We study sufficient -degree (1≤<k) conditions for the appearance of perfect and nearly perfect matchings in k-uniform hypergraphs. In particular, we obtain a minimum vertex degree condition (=1) for 3-uniform hypergraphs, which is approximately tight, by showing that every 3-uniform hypergraph on n vertices with minimum vertex degree at least (5/9+o(1))n2 contains a perfect matching.
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Hàn et al. (2009) studied this question.
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