A complete solution to the existence problem for 1‐rotational k ‐cycle systems of K v

The necessary and sufficient conditions for the existence of a 1‐rotational k ‐cycle system of the complete graph K v are established. The proof provides an algorithm able to determine, directly and explicitly, an odd k ‐cycle system of K v whenever such a system exists. © 2009 Wiley Periodicals,Inc. J Combin Designs 17: 283–293, 2009