The isomorphic factorization of complete tripartite graphs K(m, n, s) into 9 × 2~k isomorphic factors

摘要

F. Harary, R.W.Robinson and N.C.Wormald come up with the conjecture that a complete tripartite graph K(m, n, s), when t > 1, t is even, and t|(mn + ms + ns), then G has an isomorphic factorization into t isomorphic subgraphs. In this paper, with the decomposition and coresidual methods, we will show that the conjecture is true for the case that t = 9 × 2 ~k.