A counterexample to prism-hamiltonicity of 3-connected planar graphs

Abstract

The prism over a graph G is the Cartesian product of G with the complete graph K 2 . A graph G is hamiltonian if there exists a spanning cycle in G, and G is prism-hamiltonian if the prism over G is hamiltonian.In [M. Rosenfeld, D. Barnette, Hamiltonian circuits in certain prisms, Discrete Math. 5 (1973), 389-394] the authors conjectured that every 3-connected planar graph is prism-hamiltonian. We construct a counterexample to the conjecture.