Let $\vec{T}_k$ be the transitive tournament on $k$ vertices. We show that every oriented graph on $n=4m$ vertices with minimum total degree $(11/12+o(1))n$ can be partitioned into vertex disjoint $\vec{T}_4$'s, and this bound is asymptotically tight. We also improve the best known bound on the minimum total degree for partitioning oriented graphs into vertex disjoint $\vec{T}_k$'s.

Let $n$ be sufficiently large and suppose that $G$ is a digraph on $n$ vertices where every vertex has in- and outdegree at least $n/2$. We show that $G$ contains every orientation of a Hamilton cycle except, possibly, the antidirected one. The antidirected case was settled by DeBiasio and Molla, where the threshold is $n/2+1$. Our result is best possible and improves on an approximate result by Häggkvist and Thomason.

In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767--821] showed that if a 3-graph $H$ on $n$ vertices has minimum codegree at least $(1/4 +o(1))n$ and $n$ is even, then $H$ has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of $n/4$ suffices. The result is tight.