On path factorization of complete multipartite multigraphs - Wu, Zhanggui; Du, Beiliang (Utilitas Mathematica, 2010)
It is shown that the necessary conditions mn = 0 (mod k) and λ(m - 1)nk = 0 (mod 2(k - 1)) for λ(Km * K̄n), the complete multipartite multigraphs, to have a Pk-factorization are sufficient when k = p + 1 and p is prime. This answers the conjecture of Yu on Pk-factorizations of complete multipartite multigraphs, when k = prime+1.