  If $G$ is a graph and $\vec H$ is an oriented graph, we write $G\to \vec H$
to say that every orientation of the edges of $G$ contains $\vec H$ as a
subdigraph. We consider the case in which $G=G(n,p)$, the binomial random
graph. We determine the threshold $p_{\vec H}=p_{\vec H}(n)$ for the property
$G(n,p)\to \vec H$ for the cases in which $\vec H$ is an acyclic orientation of
a complete graph or of a cycle.
