Diagonally switchable 4-cycle systems revisited

A 4-cycle system is said to be diagonally switchable if each 4-cycle can be replaced by another 4-cycle obtained by replacing one pair of nonadjacent edges of the original 4-cycle by its diagonals so that the transformed set of 4-cycles forms another 4-cycle system. The existence of diagonally switchable 4-cycle system of Kv has already been solved [Adams, Bryant, Grannell and Griggs, Australas. J. Combin. 34 (2006), 145–152.] In this paper we give an alternative proof of this result and use the method to prove a new result for Kv − I, where I is any one factor of Kv.