Abstract
Our purpose is to consider the following conjectures: Conjecture 1 (Barnette). Every cubic 3-connected bipartite planar graph is Hamiltonian. Conjecture 2 (Jaeger). Every cubic cyclically 4-edge connected graph G has a cycle C such that G-V(C) is acyclic. Conjecture 3 (Jackson, Fleischner). Every cubic cyclically 4-edge connected graph G has a cycle C such that V(G)-V(C) is an independent set of vertices. We show that the previous conjectures are respectively equivalent to three other ones
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