A new linear algorithm for the two path problem on chordal graphs

Let G= (V,E) be a finite undirected graph with four distinguished vertices s, t, u, v. The two path problem (TPP) is to determine whether there exist two vertex disjoint paths connecting s with t and u with v and to find such paths if they exist. In this paper, a simple and efficient algorithm for TPP restricted to 2-connected chordal graphs is given. The reduction of TPP for a general chordal graph to the TPP for a 2-connected chordal graph is outlined.