Flows and cuts have been the topic of much study since Ford and Fulkerson's
original paper. The problem we look at is the computation of flows on some
generalizations of planar graphs. In particular, the input graph can be embedded
on a surface of genus g, and has the source and sink on the same face. We show
this problem can be reduced to a convex programming problem in dimension
2g, and also show some interesting properties of the feasible polytope.
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