Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs

We show that for all k ≤ −1 an interval graph is −(k + 1)Hamilton-connected if and only if its scattering number is at most k. We also give an O(n +m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the O(n) time bound of Kratsch, Kloks and Müller. As a consequence of our two results the maximum k for which an interval graph is kHamilton-connected can be computed in O(n+m) time.