DECOMPOSITIONS OF A COMPLETE MULTIDIGRAPH INTO ALMOST ARBITRARY PATHS 1

For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n−1 and different from n−2, unless n = 5, λ = 1, and all lengths are to be n−1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n − 2 can also be prescribed