  Given an edge-weighted undirected graph and a list of k source-sink pairs of
vertices, the well-known minimum multicut problem consists in selecting a
minimum-weight set of edges whose removal leaves no path between every source
and its corresponding sink. We give the first polynomial-time algorithm to
solve this problem in planar graphs, when k is fixed. Previously, this problem
was known to remain NP-hard in general graphs with fixed k, and in trees with
arbitrary k; the most noticeable tractable case known so far was in planar
graphs with fixed k and sources and sinks lying on the outer face.
