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Hung and Chang showed that for all k>=1 an interval graph has a path cover ofsize at most k if and only if its scattering number is at most k. They alsoshowed that an interval graph has a Hamilton cycle if and only if itsscattering number is at most 0. We complete this characterization by provingthat for all k<=-1 an interval graph is -(k+1)-Hamilton-connected if and onlyif its scattering number is at most k. We also give an O(m+n) time algorithmfor computing the scattering number of an interval graph with n vertices an medges, which improves the O(n^4) time bound of Kratsch, Kloks and M\"uller. Asa consequence of our two results the maximum k for which an interval graph isk-Hamilton-connected can be computed in O(m+n) time.

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