Graph powers and k-ordered Hamiltonicity Original Research Article

It is known that if G is a connected simple graph, then image is Hamiltonian (in fact, Hamilton-connected). A simple graph is k-ordered Hamiltonian if for any sequence image, image of k vertices there is a Hamiltonian cycle containing these vertices in the given order. In this paper, we prove that if image, then image is k-ordered Hamiltonian for every connected graph G on at least k vertices. By considering the case of the path graph image, we show that this result is sharp. We also give a lower bound on the power of the cycle image that guarantees k-ordered Hamiltonicity.