A Perfect One-Factorisation of $K_{56}$

Abstract

In 1963, Anton Kotzig conjectured that for each $n\ge 2$ the complete graph $K_{2n}$ has a perfect one-factorisation (i.e., a decomposition into perfect matchings such that each pair of perfect matchings of the decomposition induces a Hamilton cycle). We affirmatively settle the smallest unresolved case for this conjecture.