Barnette Graphs with Faces up to Size 8 are Hamiltonian

TL;DR

This paper proves that all cubic, bipartite, planar, and 2-connected graphs with faces up to size 8 are Hamiltonian, extending previous results that covered faces up to size 6, using computational methods.

Contribution

It significantly extends the class of graphs known to be Hamiltonian by proving the conjecture for faces up to size 8, involving extensive computational case analysis.

Findings

Proves Hamiltonicity for graphs with faces up to size 8

Includes analysis of over 339 million cases

Strengthens previous results for face sizes up to 6

Abstract

Barnette's conjecture states that every cubic, bipartite, planar and 3-connected graph is Hamiltonian. Goodey verified Barnette's conjecture for all graphs with faces of size up to 6. We substantially strengthen Goodey's result by proving Hamiltonicity for cubic, bipartite, planar and (2-)connected graphs with faces of size up to 8. Parts of the proof are computational, including a distinction of 339.068.624 cases.