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An O(n+m) Certifying Triconnnectivity Algorithm for Hamiltonian Graphs

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Abstract

A graph is triconnected if it is connected, has at least 4 vertices and the removal of any two vertices does not disconnect the graph. We give a certifying algorithm deciding triconnectivity of Hamiltonian graphs with linear running time (this assumes that the cycle is given as part of the input). If the input graph is triconnected, the algorithm constructs an easily checkable proof for this fact. If the input graph is not triconnected, the algorithm returns a separation pair.

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Authors and Affiliations

  1. MPI für Informatik, Campus E1 4, 66123, Saarbrücken, Germany

    Amr Elmasry & Kurt Mehlhorn

  2. Dept. of Computer Science, FU Berlin, Berlin, Germany

    Jens M. Schmidt

Authors
  1. Amr Elmasry
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  2. Kurt Mehlhorn
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  3. Jens M. Schmidt
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Corresponding author

Correspondence to Kurt Mehlhorn.

Additional information

A. Elmasry is supported by an Alexander von Humboldt Fellowship.

J.M. Schmidt’s research was supported by the Deutsche Forschungsgemeinschaft within the research training group “Methods for Discrete Structures” (GRK 1408).

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Elmasry, A., Mehlhorn, K. & Schmidt, J.M. An O(n+m) Certifying Triconnnectivity Algorithm for Hamiltonian Graphs. Algorithmica 62, 754–766 (2012). https://doi.org/10.1007/s00453-010-9481-2

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  • DOI: https://doi.org/10.1007/s00453-010-9481-2

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