  In 2009, Jonoska, Seeman and Wu showed that every graph admits a route for a
DNA reporter strand, that is, a closed walk covering every edge either once or
twice, in opposite directions if twice, and passing through each vertex in a
particular way. This corresponds to showing that every graph has an
\emph{edge-outer embedding}, that is, an orientable embedding with some face
that is incident with every edge. In the motivating application, the objective
is such a closed walk of minimum length. Here we give a short algorithmic proof
of the original existence result, and also prove that finding a shortest length
solution is NP-hard, even for $3$-connected cubic ($3$-regular) planar graphs.
Independent of the motivating application, this problem opens a new direction
in the study of graph embeddings, and we suggest new problems emerging from it.
