A family of perfect factorisations of complete bipartite graphs
A 1-factorization of a graph is called perfect if the union of any two of its 1-factors is a single (Hamiltonian) cycle. A Latin square is pan-Hamiltonian if the permutation determined by any pair of rows yields a single cycle. Let \(p\) be any odd prime and let \(n= p^2\). The authors construct \((p-1)/2\) non-isotopic pan-Hamiltonian Latin squares of order \(n\). Equivalently, this yields a family of \((p-1)/2\) non-isomorphic perfect 1-factorizations of the complete bipartite graph \(K_{n,n}\), thereby establishing existence for infinitly many new values of \(n\).
scientific article; zbMATH DE number 1760684