A Note on Barnette’s Conjecture

  title={A Note on Barnette’s Conjecture},
  author={Jochen Harant},
  booktitle={Discuss. Math. Graph Theory},
  • J. Harant
  • Published in Discuss. Math. Graph Theory 1 March 2013
  • Mathematics
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. 

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