  Given a graph, does there exist an orientation of the edges such that the
resulting directed graph is strongly connected?
  Robbins' theorem [Robbins, Am. Math. Monthly, 1939] states that such an
orientation exists if and only if the graph is $2$-edge connected. A natural
extension of this problem is the following: Suppose that the edges of the graph
is partitioned into trails. Can we orient the trails such that the resulting
directed graph is strongly connected?
  We show that $2$-edge connectivity is again a sufficient condition and we
provide a linear time algorithm for finding such an orientation, which is both
optimal and the first polynomial time algorithm for deciding this problem.
  The generalised Robbins' theorem [Boesch, Am. Math. Monthly, 1980] for mixed
multigraphs states that the undirected edges of a mixed multigraph can be
oriented making the resulting directed graph strongly connected exactly when
the mixed graph is connected and the underlying graph is bridgeless. We show
that as long as all cuts have at least $2$ undirected edges or directed edges
both ways, then there exists an orientation making the resulting directed graph
strongly connected. This provides the first polynomial time algorithm for this
problem and a very simple polynomial time algorithm to the previous problem.
