Rotational k-cycle systems of order ν < 3k;: Another proof of the existence of odd cycle systems

We give an explicit solution to the existence problem for 1-rotational k-cycle systems of order nu < 3k with k odd and nu not equal 2k + 1. We also exhibit a 2-rotational k-cycle system of order 2k + 1 for any odd k. Thus, for k odd and any admissible nu < 3k there exists a 2-rotational k-cycle system of order nu. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient. (C) 2003 Wiley Periodicals, Inc.