Article ID: | iaor2012410 |
Volume: | 62 |
Issue: | 3 |
Start Page Number: | 754 |
End Page Number: | 766 |
Publication Date: | Apr 2012 |
Journal: | Algorithmica |
Authors: | Mehlhorn Kurt, Schmidt Jens, Elmasry Amr |
Keywords: | optimization |
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.