A Note on Barnette’s Conjecture
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 133.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 05C10, 05C38, 05C40, 05C45
Mots-clés : planar graph, Hamilton cycle, Barnette’s Conjecture, Barnette's conjecture 
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Jochen Harant. A Note on Barnette’s Conjecture. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 133. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267635/