Perfect 1-factorisations of $K_{18}$ with a non-trivial automorphism group

Andrei V. Ivanov, Leonid M. Tertitski

A perfect 1-factorisation (P1F) of $K_{2n}$ is a partition of its edges into $2n-1$ perfect matchings, any two of which form a Hamiltonian cycle. Exhaustive classification is known…