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Context: Barnette's Conjecture is that every bipartite cubic polyhedral graph is Hamiltonian. I have been interested by this problem for a long time, and I recently came up with a result. From my ...

Does anyone know whether bipartite symmetric graphs are hamiltonian? I'm not sure whether anyone have proved it before, but a nonhamiltonian symmetric bipartite graph would lead to a counterexample to ...

Fleischner mentions in his article Uniqueness of maximal dominating cycles in 3-regular graphs and of hamiltonian cycles in 4-regular graphs about the uniqueness of compatible cycle decomposition that ...