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 3) time bound of Kratsch, Kloks and Müller. As a consequence of our two results the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n + m) time