Perfect 1-factorisations of K11,11
A perfect 1-factorisation of a graph is a decomposition of that
graph into 1-factors such that the union of any two 1-factors is
a Hamiltonian cycle. A Latin square of order n is row-Hamiltonian
if for every pair (r,s) of distinct rows, the permutation mapping
r to s has a single cycle of length n. We report the results
of a computer enumeration of the perfect 1-factorisations of the
complete bipartite graph K11,11. This also allows us to find
all row-Hamiltonian Latin squares of order 11. Finally, we plug a
gap in the literature regarding how many row-Hamiltonian Latin
squares are associated with the classical families of perfect
1-factorisations of complete graphs.