On the structure of uniform one-factorizations from starters in finite fields

It is known that the Horton starters can be used to construct uniform one-factorizations of the complete graph. Of primary interest is the cycle structure of such one-factorizations. In this paper we give some general conditions for the existence of k-cycles, then specialize this to the cases k=4,6, completely characterizing the four-cycle case. We also show that for each even k>4 and any positive integer N there exists a uniform one-factorization in some large enough complete graph containing at least N k-cycles.