@article{, AUTHOR = {Harant, Jochen}, TITLE = {A note on Barnette's Conjecture}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {33}, YEAR = {2013}, NUMBER = {1}, PAGES = {133137}, ISSN = {12343099}, 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.
}, }
