Minimum Codegree Threshold for C₆³-Factors in 3-Uniform Hypergraphs

Let C₆³ be the 3-uniform hypergraph on {1,..., 6} with edges 123,345,561, which can be seen as the analogue of the triangle in 3-uniform hypergraphs. For sufficiently large n divisible by 6, we show that every n-vertex 3-uniform hypergraph H with minimum codegree at least n/3 contains a C₆³-factor, that is, a spanning subhypergraph consisting of vertex-disjoint copies of C₆³. The minimum codegree condition is best possible. This improves the asymptotic result obtained by Mycroft and answers a question of Rödl and Ruciński exactly.