Irreducible 2-fold cycle systems

摘要

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.