Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian

Sihong Shao; Yuxuan Wu

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arXiv · 2504.20706

Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian

Sihong Shao·Yuxuan Wu

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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.

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Sihong Shao, Yuxuan Wu. 2025-04-29. Every 2-connected, cubic, planar graph with faces of size at most 6 is Hamiltonian. https://arxiv.org/abs/2504.20706

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