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

Authors:
Amr Elmasry;Kurt Mehlhorn;Jens M. Schmidt
Affiliations:
MPI für Informatik, Campus E1 4, 66123, Saarbrücken, Germany;MPI für Informatik, Campus E1 4, 66123, Saarbrücken, Germany;FU Berlin, Dept. of Computer Science, Berlin, Germany
Venue:
Algorithmica
Year:
2012

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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.