Irreducible 2‐fold cycle systems

In this paper, it is shown that for any pair of integers (m,n) with 4 ≤ m ≤ n, if there exists an m‐cycle system of order n, then there exists an irreducible 2‐fold m‐cycle system of order n, except when (m,n) = (5,5). A similar result has already been established for the case of 3‐cycles. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 324–332, 2006