Py-factorization of Symmetric Complete Bipartite Digraphs

摘要

Let Pv be the directed path on v vertices and K~tn be the symmetric complete bipartite digraph with two partite sets having m and n vertices. A Pv-factorization of K~n is a set of arc-disjoint P,,-factors of Km,n which is a partition of the set of arcs of Km.n.' When v is an even number, the spectrum problem for a Pv-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,,-factorization of K~.n for v is an odd number.