Technical Report CS0585

Title: On Disjoint Paths Problems in Graphs With Bounded Tree Width
Authors: E. Korach, N. Sole1 and A. Tal
Abstract: The vertex disjoint connecting paths problem is dermed as follows: Given an undirected graph G=(V,E) and k pairs of vertices of V - (source,sink), find whether G contains k internally vertex disjoint paths, one connecting each pair. Karp has shown that this problem is NP-complete (even when all sources and sinks are distinct), and Robertson and Seymour solved this problem where the number of paths is constant. For graphs with bounded tree width we solve in polynomial time a version of this problem: k is a part of the input and only the number of sinks in a vertex is bounded. We also solve some more problems related to the disjoint connecting paths problem on graphs with bounded tree width.
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