Multiple hamiltonian covers

The aim of this work is to introduce the concept of a multiple hamiltonian cover ( M HC) for regular graphs. By means of several examples we hope to convey some of the difficulties encountered when searching for an M HC. For the most part efforts shall be restricted to the cases when the graphs are cubic, three–connected and planar and where the ( M HC) consists of either three or six hamiltonian cycles only. In the first of these cases we are able to derive a Grinberg type theorem. In the second case it is convenient to impose an additional condition which then leads us to the concept of a balanced M HC, which has some interesting properties. Finally we conclude with the solution of a non–trivial problem in three–dimensional geometry through the use of M HCʹs.