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arXiv · 2506.20086

Minors of non-hamiltonian polyhedra and the Herschel family

On-Hei Solomon Lo·Kenta Ozeki
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Abstract

We show that every non-hamiltonian polyhedron contains the Herschel graph as a minor, implying that the Herschel graph is the unique minor-minimal non-hamiltonian polyhedron. Our approach unifies many previously known results on minors of non-hamiltonian polyhedra, while strengthening them with significantly shorter, non-computer-assisted proofs. As an application, we characterize non-hamiltonian polyhedra with no $K_{2,6}$ minor, resolving a conjecture of Ellingham, Marshall, and Royle.

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On-Hei Solomon Lo, Kenta Ozeki. 2026-08-21. Minors of non-hamiltonian polyhedra and the Herschel family. https://arxiv.org/abs/2506.20086

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