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Linear-time algorithms for scattering number and Hamilton-connectivity of interval graphs.

Broersma, H.J. and Fiala, J. and Golovach, P.A. and Kaiser, T. and Paulusma, D. and Proskurowski, A. (2013) 'Linear-time algorithms for scattering number and Hamilton-connectivity of interval graphs.', in Graph-theoretic concepts in computer science : 39th International Workshop, WG 2013, 19-21 June 2013, Lübeck, Germany ; revised papers. Berlin, Heidelberg: Springer, pp. 127-138. Lecture notes in computer science. (8165).


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.

Item Type:Book chapter
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Date accepted:No date available
Date deposited:15 January 2015
Date of first online publication:2013
Date first made open access:No date available

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