Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian
Combinatorics
2025-04-30 v1
Abstract
We prove that every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian, and show that the 6-face condition is tight. Our results push the connectivity condition of the Barnette-Goodey conjecture to the weakest possible.
Keywords
Cite
@article{arxiv.2504.20706,
title = {Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian},
author = {Sihong Shao and Yuxuan Wu},
journal= {arXiv preprint arXiv:2504.20706},
year = {2025}
}