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Linear Time Algorithms for Hamiltonian Problems on (Claw,Net)—Free Graphs

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Graph-Theoretic Concepts in Computer Science (WG 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

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Abstract

We prove that claw-free graphs, containing an induced dominating path, have a Hamiltonian path, and that two-connected claw-free graphs, containing an induced doubly dominating cycle or a pair of vertices such that there exist two internally disjoint induced dominating paths connecting them, have a Hamiltonian cycle. As a consequence, we obtain linear time algorithms for both problems if the input is restricted to (claw,net)-free graphs. These graphs enjoy those interesting structural properties.

Research of the second author supported by the DFG. Research of the third author supported by the graduate program ‘Algorithmic Discrete Mathematics’, grant GRK 219/2-97 of the German National Science Foundation (DFG).

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Rostock, A. Einstein Str. 21, D-18051, Rostock, Germany

    Andreas Brandstädt & Feodor F. Dragan

  2. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Ekkehard Köhler

Authors
  1. Andreas Brandstädt
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  2. Feodor F. Dragan
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  3. Ekkehard Köhler
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Brandstädt, A., Dragan, F.F., Köhler, E. (1999). Linear Time Algorithms for Hamiltonian Problems on (Claw,Net)—Free Graphs. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_34

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  • DOI: https://doi.org/10.1007/3-540-46784-X_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

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