  Huggett and Moffatt characterized all bipartite partial duals of a plane
graph in terms of all-crossing directions of its medial graph. Then Metsidik
and Jin characterized all Eulerian partial duals of a plane graph in terms of
semi-crossing directions of its medial graph. Plane graphs are ribbon graphs
with genus 0. In this paper, we shall first extend Huggett and Moffatt's result
to any orientable ribbon graph and provide an example to show that it is not
true for non-orientable ribbon graphs. Then we characterize all Eulerian
partial duals of any ribbon graph in terms of crossing-total directions of its
medial graph, which are much more simple than semi-crossing directions.
