Minimum Codegree Threshold forC63-Factors in 3-Uniform Hypergraphs

Abstract

LetC63be 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 largendivisible by 6, we show that everyn-vertex 3-uniform hypergraphHwith minimum codegree at leastn/3 contains aC63-factor, that is, a spanning subhypergraph consisting of vertex-disjoint copies ofC63. The minimum codegree condition is best possible. This improves the asymptotic result obtained by Mycroft and answers a question of Rödl and Ruciński exactly.