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

Haitze J. Broersma, Jiri Fiala, Petr A. Golovach, Tomas Kaiser, Daniël Paulusma, Andrzej Proskurowski

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We prove that for all integers k<0 an interval graph is -(k+1)-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 O(n+m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known O(n^3) 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 O(n+m) time.
Original languageUndefined
Pages (from-to)282-299
Number of pages18
JournalJournal of graph theory
Issue number4
Publication statusPublished - Aug 2015


  • MSC-05C
  • METIS-314967
  • IR-98274
  • EWI-26316

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