Hamiltonicity of planar graphs with a forbidden minor.

Tutte showed that 4-connected planar graphs are Hamiltonian, but it is well known that 3-connected planar graphs need not be Hamiltonian. We show that K2,5-minor-free 3-connected planar graphs are Hamiltonian. This does not extend to K2,5-minor-free 3-connected graphs in general, as shown by the Petersen graph, and does not extend to K2,6-minor-free 3-connected planar graphs, as we show by an infinite family of examples.