Some basic properties of multiple Hamiltonian covers

The aim of this work is to introduce the concept of a multiple Hamiltonian cover  (MHC)(MHC). For the most part, attention is restricted to the class of cubic three-connected planar graphs. For those graphs having an MHCMHC composed of three Hamiltonian cycles we are able to derive a Grinberg type result. On the other hand, for those graphs having an MHCMHC 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. MHCMHC's play a significant role in its solution.