Cyclic bundle Hamiltonicity ## AbstractCyclic bundle Hamiltonicity cbH(G) of a graph G is the minimal n for which there is an automorphism α of G such that the graph bundle C n □α G is Hamiltonian. We define an invariant I that is related to the maximal vertex degree of spanning trees suitably involving the symmetries of G and prove cbH(G)≤I≤cbH(G)+1 for any non-trivial connected graph G.
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