Barnette Graphs with Faces up to Size 8 are Hamiltonian
Combinatorics
2025-08-06 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2508.03531,
title = {Barnette Graphs with Faces up to Size 8 are Hamiltonian},
author = {Tobias Schnieders},
journal= {arXiv preprint arXiv:2508.03531},
year = {2025}
}
Comments
16 pages, 56 figures