GENERAL VERTEX DISJOINT PATHS IN SERIES-PARALLEL GRAPHS

Let G = (V,E) be an undirected graph and let (s(i),t(i)), 1 less-than-or-equal-to i less-than-or-equal-to k be k pairs of vertices in G. The vertex disjoint paths problem is to find k paths P(l), ..., P(k) such that P(i) connects s(i) and t(i) and any two of these paths may intersect only at a common endpoint. This problem is NP-complete even for planar graphs. Robertson and Seymour proved that when k is a fixed integer this problem becomes polynomial. We present a linear time algorithm for solving the decision version of the general problem when the input graph is a series-parallel graph.