A family of perfect factorisations of complete bipartite graphs
A 1-factorisation of a graph is perfect if the union of any two of its
1-factors is a Hamiltonian cycle. Let n=p2 for an odd prime p.
We construct a family of (p-1)/2 non-isomorphic perfect
1-factorisations of Kn,n. Equivalently, we construct
pan-Hamiltonian Latin squares of order n. A Latin square is
pan-Hamiltonian if the permutation defined by any row relative to any
other row is a single cycle.
Click here to download the whole paper.