Exact Minimum Codegree Threshold for K4--Factors

Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K-4(-) denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n is an element of 4N, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2 - 1 contains a K-4(-)-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markstrom [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.