Isomorphic factorizations VII. Regular graphs and tournaments

It is shown using enumeration results that for r > 2t, almost all labeled r-regular graphs cannot be factorized into t ? 2 isomorphic subgraphs. However, no examples of such nonfactorizable graphs are known which satisfy the obvious divisibility condition that the number of edges is divisible by t. Similar observations hold for regular tournaments (t ? 2} and for r-regular digraphs (r > t ? 2).