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We study the existence of hamiltonian cycles in plane cubic graphs G having afacial 2-factor Q. Thus hamiltonicity in G is transformed into the existence ofa (quasi) spanning tree of faces in the contraction G/Q. In particular, westudy the case where G is the leapfrog extension (called vertex envelope in(Discrete Math., 309(14):4793-4809, 2009)) of a plane cubic graph G_0. As aconsequence we prove hamiltonicity in the leapfrog extension of planar cubiccyclically 4-edge-connected bipartite graphs. This and other results of thispaper establish partial solutions of Barnette's Conjecture according to whichevery 3-connected cubic planar bipartite graph is hamiltonian. These results goconsiderably beyond Goodey's result on this topic (Israel J. Math., 22:52-56,1975).

Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture