P3-factorization of complete multipartite graphs

In this paper, it is shown that a necessary and sufficient condition for the existence of aP3-factorization ofKmn is (i)mn ≡ 0(mod 3) and (ii) (m − 1)n ≡ 0(mod 4).

[1]  Kazuhiko Ushio.  P3-Factorization of complete bipartite graphs , 1988, Discret. Math..

[2]  Joseph Douglas Horton.  Resolvable Path Designs , 1985, J. Comb. Theory, Ser. A.