Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes

Fullerene graphs, i.e., 3-connected planar cubic graphs with pentagonal and hexagonal faces, are conjectured to be Hamiltonian. This is a special case of a conjecture of Barnette and Goodey, stating that 3-connected planar cubic graphs with faces of size at most 6 are Hamiltonian. We prove Barnette and Goodey's conjecture.

Automated summary

This article translates and summarizes the conjecture and proof of the Hamiltonian property in 3-connected planar cubic graphs.