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

Published 29 Apr 2025 in math.CO | (2504.20706v1)

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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