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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.
Hàn et al. (Thu,) studied this question.