Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (si,ti) contains paths P1,...,Pk such that Pi connects si and ti for i=1,...,k, and Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their ends) for 1<=i < j<=k. We present a linear-time algorithm for Induced Disjoint Paths on circular-arc graphs. For interval graphs, we exhibit a linear-time algorithm for the generalization of Induced Disjoint Paths where the pairs (si,t_i) are not necessarily distinct.