# Hamiltonian circuits on 3-polytopes

```@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}
}```
• Published 1 July 1970
• Mathematics, Physics
• Journal of Combinatorial Theory, Series A
24 Citations
Polyhedra without cubic vertices are prism-hamiltonian
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
A pr 2 02 1 Polyhedra without cubic vertices are prism-hamiltonian
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
Shortness Exponents of Families of Graphs
• Mathematics
J. Comb. Theory, Ser. A
• 1973
Planar graphs, Hamilton cycles and extreme independence number
This work shows how to construct graphs near the threshold: they have as many edges as possible without sacrificing planarity but are not Hamiltonian.
Circumference of essentially 4-connected planar triangulations
• Mathematics
J. Graph Algorithms Appl.
• 2021
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.
On the number of hamiltonian cycles in a maximal planar graph
• Mathematics
J. Graph Theory
• 1979
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.
An upper bound on the length of a Hamiltonian walk of a maximal planar graph
• Mathematics
J. Graph Theory
• 1980
It is shown that every maximal planar graph with p(≥ 3) vertices has aHamiltonian cycle or a Hamiltonian walk of length ≤ 3(p - 3)/2.
Hamiltonicity of planar graphs with a forbidden minor
• Mathematics
J. Graph Theory
• 2019
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.