A note on some embedding problems for oriented graphs

We conjecture that every oriented graph G on n vertices with δ⁺(G), δ^?(G)≥5n/12 contains the square of a Hamilton cycle. We also give a conjectural bound on the minimum semidegree which ensures a perfect packing of transitive triangles in an oriented graph. A link between Ramsey numbers and perfect packings of transitive tournaments is also considered. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 330–336, 2012