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
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8165)

Abstract

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(n3) 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hajo Broersma
    • 1
  • Jiří Fiala
    • 2
  • Petr A. Golovach
    • 3
  • Tomáš Kaiser
    • 4
  • Daniël Paulusma
    • 5
  • Andrzej Proskurowski
    • 6
  1. 1.Faculty of EEMCSUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of Applied MathematicsCharles UniversityPragueCzech Republic
  3. 3.Institute of Computer ScienceUniversity of BergenNorway
  4. 4.Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic
  5. 5.School of Engineering and Computing SciencesDurham UniversityUK
  6. 6.Department of Computer ScienceUniversity of OregonEugeneUSA

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