A note on some embedding problems for oriented graphs

Abstract

We conjecture that every oriented graph $G$ on $n$ vertices with ${\delta }^{+}(G),{\delta }^{-}(G)\ge 5n/12$ 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.

6 pages, 2 figures

References in corpus (1)

• A survey on Hamilton cycles in directed graphs