Cyclic one-factorization of the complete graph (Q1092066)

Let \(K_ n\) be the complete graph of order n with vertex set V and edge set E. A 1-factorization of \(K_ n\) is a partition of E into n-1 one factors, so that each 1-factor is a partition of V. An automorphism of a 1-factorization is a permutation of V which maps 1-factors onto 1- factors. A 1-factorization is cyclic if it admits an n-cycle as an automorphism. In this paper the authors show that cyclic 1-factorizations exists if and only if n is even and \(n\neq 2^ t\), \(t\geq 3\). They also enumerate cyclic 1-factorizations of \(K_ n\) for \(n\leq 16\).