Discussiones Mathematicae Graph Theory 33(1) (2013) 133-137
doi: 10.7151/dmgt.1643

Dedicated to M. Borowiecki on the occasion of his 70th birthday

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A Note on Barnette's Conjecture

Jochen Harant

Institut für Mathematik, TU Ilmenau
D-98684 Ilmenau, Germany

Abstract

Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c > 0 such that each graph G of this class contains a path on at least c |V(G) | vertices.

Keywords: planar graph, Hamilton cycle, Barnette's Conjecture

2010 Mathematics Subject Classification: 05C38, 05C40, 05C45.

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Received 14 March 2012
Revised 15 August 2012
Accepted 20 August 2012