Cyclic Triangle Factors in Regular Tournaments

Both Cuckler and Yuster independently conjectured that when n is an odd positive multiple of $3$ every regular tournament on n vertices contains a collection of $n/3$ vertex-disjoint copies of the cyclic triangle. Soon after, Keevash & Sudakov proved that if G is an orientation of a graph on n vertices in which every vertex has both indegree and outdegree at least $(1/2 - o(1))n$, then there exists a collection of vertex-disjoint cyclic triangles that covers all but at most $3$ vertices. In this paper, we resolve the conjecture of Cuckler and Yuster for sufficiently large n.