The sufficiency of the divisibility condition for 6 × 2k divides complete tripartite graph K(m, n, s). (3rd March 2016) - Duan, Huiming; Min, Zijian; Yang, Jinchen
Abstract: In this paper, we will use the decomposition and congruence methods, and proved the conjecture when t = 6 × 2 k, and the conjecture that G has an isomorphic factorization into t isomorphic subgraphs. The conjecture was proposed by Harary, Robinson and Wormald, and when t = 2, 4 and t | ( mn + ms + ns ), they proved a complete tripartite graph G = K ( m, n, s ) if t = 2, 4 and t | ( mn + ms + ns ), and for all odd t > 1, the divisibility condition is false to be a sufficient condition for t | (1, 1, m ).