The number of $6$-cycles in $2$-factorizations of $K_n$, $n$ odd

Abstract

In this paper, we construct 2-factorizations of $K_n$ ($n$ odd) containing a specified number, $k$, of 6-cycles, for all integers $k$ between 0 and the maximum possible expected number of 6-cycles in any 2-factorization, and for all odd $n$, with no exceptions.