# A Note on Barnette’s Conjecture

@inproceedings{Harant2013ANO, title={A Note on Barnette’s Conjecture}, author={Jochen Harant}, booktitle={Discuss. Math. Graph Theory}, year={2013} }

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.

## 4 Citations

### Construction of Barnette graphs whose large subgraphs are non-Hamiltonian

- Mathematics
- 2019

Abstract Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in…

### Thoughts on Barnette's Conjecture

- MathematicsAustralas. J Comb.
- 2016

A new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian is proved, which implies the following special case of Barnette's Conjecture: if G is an Eulerian planar triangulation, whose vertices are properly coloured blue, red and green, then $G^*$ is Hamiltonian.

### A Relationship Between Thomassen's Conjecture and Bondy's Conjecture

- MathematicsSIAM J. Discret. Math.
- 2015

It is shown that Bondy's conjecture implies a slightly weaker version of Thomassen's conjecture: every 4-connected line graph with minimum degree at least 5 has a Hamiltonian cycle.

### On Barnette’s conjecture and the $$H^{+-}$$H+- property

- MathematicsJ. Comb. Optim.
- 2016

It is proved that if every cyclic sequence of big faces has a face belonging to X and Y and a face belong to $$Y$$Y, then G∗ has a Hamilton cycle.

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