H.J. Broersma
Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs
Broersma, H.J.; Fiala, J.; Golovach, P.A.; Kaiser, T.; Paulusma, D.; Proskurowski, A.
Authors
J. Fiala
P.A. Golovach
T. Kaiser
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
A. Proskurowski
Abstract
We prove that for all inline image an interval graph is inline image-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an inline image time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known inline image time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in inline image time.
Citation
Broersma, H., Fiala, J., Golovach, P., Kaiser, T., Paulusma, D., & Proskurowski, A. (2015). Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs. Journal of Graph Theory, 79(4), 282-299. https://doi.org/10.1002/jgt.21832
Journal Article Type | Article |
---|---|
Online Publication Date | Oct 28, 2014 |
Publication Date | Aug 1, 2015 |
Deposit Date | Dec 20, 2014 |
Publicly Available Date | Jan 8, 2015 |
Journal | Journal of Graph Theory |
Print ISSN | 0364-9024 |
Electronic ISSN | 1097-0118 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 79 |
Issue | 4 |
Pages | 282-299 |
DOI | https://doi.org/10.1002/jgt.21832 |
Public URL | https://durham-repository.worktribe.com/output/1439478 |
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Copyright Statement
Broersma, H.J. and Fiala, J. and Golovach, P.A. and Kaiser, T. and Paulusma, D. and Proskurowski, A. (2014) 'Linear-time algorithms for scattering number and Hamilton-connectivity of interval graphs.', Journal of graph theory, 79(4): 282-299, which has been published in final form at http://dx.doi.org/10.1002/jgt.21832. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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