Two Perfect One-Factorizations of $K_{92}$

Abstract

A perfect 1-factorization of the complete graph $K_{2t}$ is a partition of its edges into perfect matchings such that the union of any two of them is a Hamilton cycle. Kotzig conjectured in 1963 that $K_{2t}$ has a perfect 1-factorization for every $t \ge 2$, but apart from some infinite families and a list of sporadic orders the conjecture is open, and $92$ was one of the nine orders up to $100$ for which no perfect 1-factorization was known. In this paper we construct two non-isomorphic perfect 1-factorizations of $K_{92}$.