A Note on Barnette’s Conjecture - Harant Jochen (Discussiones Mathematicae Graph Theory, 2013)
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.