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arXiv · 1301.5953

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

Hajo Broersma·Jiří Fiala·Petr A. Golovach·Tomáš Kaiser·Daniël Paulusma·Andrzej Proskurowski
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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.

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Hajo Broersma, Jiří Fiala, Petr A. Golovach, Tomáš Kaiser, Daniël Paulusma, Andrzej Proskurowski. 2013-01-25. Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs. https://arxiv.org/abs/1301.5953

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