Abstract
We study the existence of hamiltonian cycles in plane cubic graphs G having a facial 2‐factor Q. Thus hamiltonicity in G is transformed into the existence of a (quasi) spanning tree of faces in the contraction G∕Q. In particular, we study the case where G is the leapfrog extension (called vertex envelope of a plane cubic graph G0. As a consequence we prove hamiltonicity in the leapfrog extension of planar cubic cyclically 4‐edge‐connected bipartite graphs. This and other results of this paper establish partial solutions of Barnette's Conjecture according to which every 3‐connected cubic planar bipartite graph is hamiltonian. These results go considerably beyond Goodey's result on this topic.
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