@article{Barnette1970HamiltonianCO,
title={Hamiltonian circuits on 3-polytopes},
author={David W. Barnette and Ernest Jucovic},
journal={Journal of Combinatorial Theory, Series A},
year={1970},
volume={9},
pages={54-59}
}

The prism over a graphG is the Cartesian product ofG with the complete graph on two vertices. A graph G is prism-hamiltonian if the prism overG is hamiltonian. We prove that every polyhedral graph… Expand

The prism over a graphG is the Cartesian product ofG with the complete graph on two vertices. A graph G is prism-hamiltonian if the prism overG is hamiltonian. We prove that every polyhedral graph… Expand

This work shows how to construct graphs near the threshold: they have as many edges as possible without sacrificing planarity but are not Hamiltonian.Expand

It is proved that every essentially 4-connected maximal planar graph G on n vertices contains a cycle of length at least 2 3 (n+ 4); moreover, this bound is sharp.Expand

A p-vertex maximal planar graph containing exactly four Hamiltonian cycles for every p ≥ 12 vertices is constructed and it is proved that every 4-connected maximalPlanar graph on p vertices contains at least p/(log2 p) Hamiltoniancycles.Expand

It is shown that K_{2,5}-minor-free $3-connected planar graphs are Hamiltonian, and this does not extend to $K{2,6}$-miner-free £3-connecting graphs in general, as shown by the Petersen graph.Expand