Multicut is FPT

Let G=(V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is cut by F, i.e. every xy-path of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a multicut of size at most k. In other words, the Multicut problem parameterized by the solution size k is Fixed-Parameter Tractable.