Let s1, t1,. . . sk, tk be vertices in a graph G embedded on a surface \sigma
of genus g. A vertex v of G is "redundant" if there exist k vertex disjoint
paths linking si and ti (1 \lequal i \lequal k) in G if and only if such paths
also exist in G - v. Robertson and Seymour proved in Graph Minors VII that if v
is "far" from the vertices si and tj and v is surrounded in a planar part of
\sigma by l(g, k) disjoint cycles, then v is redundant. Unfortunately, their
proof of the existence of l(g, k) is not constructive. In this paper, we give
an explicit single exponential bound in g and k
