Consider simple bridgeless cubic planar graphs. Does each such graph admit a 2-factorization with 2 (or less) components each of which has even length? (If not, does anyone know of an counter-example?)

Stated otherwise, each simple bridgeless cubic planar graph is either Hamiltonian or admits a 2-factorization each of which component has even length. Is there an upper bound of the number of components?