Graph Theory With Applications
Graph Theory With Applications
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The aim of this work is to introduce the concept of a multiple Hamiltonian cover (MHC). For the most part, attention is restricted to the class of cubic three-connected planar graphs. For those graphs having an MHC composed of three Hamiltonian cycles we are able to derive a Grinberg type result. On the other hand, for those graphs having an MHC consisting of six Hamiltonian cycles we find it convenient to impose the additional notion of balance, which then allows us to deduce some interesting consequences. We conclude with a problem from three-dimensional geometry. MHC's play a significant role in its solution.