  We consider the problem of multicommodity flows in planar graphs. Seymour
showed that if the union of supply and demand graphs is planar, then the cut
condition is sufficient for routing demands. Okamura-Seymour showed that if all
demands are incident on one face, then again cut condition is sufficient for
routing demands. We consider a common generalization of these settings where
the end points of each demand are on the same face of the planar graph. We show
that if the source sink pairs on each face of the graph are such that sources
and sinks appear contiguously on the cycle bounding the face, then the flow cut
gap is at most 3. We come up with a notion of approximating demands on a face
by convex combination of laminar demands to prove this result.
