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Perfect Matching in $k$-Partite $k$-Uniform Hypergraphs
A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph whose vertex set is partitioned into $k$ classes of the same size and whose edges meet every class in exactly one vertex. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings when $k=3$, and Lu, Wang
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