A characterization of graphs with no K3,4 minor
Abstract
A complete structural characterization of graphs with no K3,4 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 K3,4 and K6- as minors, thereby proving a conjecture of Kawarabayashi and Maharry in a strengthened form. Moreover, every 4-connected graph with no K3,4 minor is hamiltonian-connected, extending a theorem of Thomassen, and admits an embedding on the torus.
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