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Algorithmica

, Volume 62, Issue 3–4, pp 754–766 | Cite as

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

  • Amr Elmasry
  • Kurt Mehlhorn
  • Jens M. Schmidt
Article

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.

Keywords

Graph algorithms Certifying algorithms Triconnectivity Hamiltonian graph 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MPI für InformatikSaarbrückenGermany
  2. 2.Dept. of Computer ScienceFU BerlinBerlinGermany

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