FACTORIZATIONS OF PRODUCT GRAPHS INTO CYCLES OF UNIFORM LENGTH

The following question is raised by Alspach, Bermond and Sotteau: If G(1) has a decomposition into hamilton cycles and a 1-factor, and G(2) has a hamilton cycle decomposition (HCD), does their wreath product G(1) * G(2) admit a hamilton cycle decomposition? In this paper the above question is answered with an additional condition on G(1). Further it is shown that some product graphs can be decomposed into cycles of uniform length, that is, the edge sets of the graphs can be partitioned into cycles of length k, for some suitable k.