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arXiv · 2603.27973

A characterization of graphs with no $K_{3,4}$ minor

On-Hei Solomon Lo
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Abstract

A complete structural characterization of graphs with no $K_{3,4}$ minor is obtained, and the following consequences are established. Every $4$-connected non-planar graph with at least seven vertices and minimum degree at least five contains both $K_{3,4}$ and $K_6^-$ as minors, thereby proving a conjecture of Kawarabayashi and Maharry in a strengthened form. Moreover, every $4$-connected graph with no $K_{3,4}$ minor is hamiltonian-connected, extending a theorem of Thomassen, and admits an embedding on the torus.

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On-Hei Solomon Lo. 2026-03-30. A characterization of graphs with no $K_{3,4}$ minor. https://arxiv.org/abs/2603.27973

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