  We consider an undirected multi(commodity)flow demand problem in which a
supply graph is planar, each source-sink pair is located on one of three
specified faces of the graph, and the capacities and demands are integer-valued
and Eulerian. It is known that such a problem has a solution if the cut and
(2,3)-metric conditions hold, and that the solvability implies the existence of
an integer solution. We develop a purely combinatorial strongly polynomial
solution algorithm.
