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Fullerene graphs, i.e., 3-connected planar cubic graphs with pentagonal andhexagonal faces, are conjectured to be Hamiltonian. This is a special case of aconjecture of Barnette and Goodey, stating that 3-connected planar graphs withfaces of size at most 6 are Hamiltonian. We prove the conjecture.

A computer-assisted proof of Barnette-Goodey conjecture: Not only fullerene graphs are Hamiltonian