P→v-factorization of symmetric complete bipartite digraphs - Wang, Jian; Du, Beiliang (Utilitas Mathematica, 2007)
Let P→v be the directed path on v vertices and K m,n* be the symmetric complete bipartite digraph with two partite sets having m and n vertices. A P→v-factorization of Km,n* is a set of arcdisjoint P→v-factors of Km,n* which is a partition of the set of arcs of K m,n*. When v is an even number, the spectrum problem for a P→v-factorization of Km,n* has been completely solved (see [4]). In this paper, it is shown that a necessary and sufficient condition for the existence of a P→v-factorization of K m,n* for v is an odd number.