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A conjecture of Alspach and Rosenfeld states that the prism G□K2 over any 3-connected cubic graph G has a decomposition into two Hamilton cycles. Using a method based on colored diagrams, we show this conjecture to hold for 3-connected planar bipartite cubic graphs and for one other class of planar cubic graphs known as ‘kleetope duals’. We also give a new proof of the fact that G□K2 is hamiltonian...
A successful heuristic algorithm for finding Hamilton cycles in cubic graphs is described. Several graphs from The Foster Census of connected symmetric trivalent graphs and all cubic Cayley graphs of the group PSL2(7) are shown to be Hamiltonian.
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