Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs
Data Structures and Algorithms
2013-01-28 v1
Abstract
Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most 0. We complete this characterization by proving 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(m+n) time algorithm for computing the scattering number of an interval graph with n vertices an m edges, which improves the O(n^4) time bound of Kratsch, Kloks and M\"uller. As a consequence of our two results the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(m+n) time.
Cite
@article{arxiv.1301.5953,
title = {Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs},
author = {Hajo Broersma and Jiří Fiala and Petr A. Golovach and Tomáš Kaiser and Daniël Paulusma and Andrzej Proskurowski},
journal= {arXiv preprint arXiv:1301.5953},
year = {2013}
}