The isomorphic factorization of complete tripartite graphs K ( m, n, s) - a proof of F. Harary, R.W. Robinson and N.C. Wormald's conjecture

Abstract

Harary, Robinson and Wormald (1978) proved that for a complete tripartite graph G = K ( m, n, s) if t = 2 or 4 and t | ( mn + ms + ns), then G has an isomorphic factorization into t isomorphic subgraphs, written as t | G. They also proved that the analogous statement is false for all odd t > 1. They conjecture that when t > 1 is even, and t |( mn + ms + ns), G = K( m, n, s), then t | G. In this paper we shall show that the conjecture is true.