The sufficiency of the divisibility condition for 6 × 2k divides complete tripartite graph K(m, n, s). (3rd March 2016)

• Record Type: Journal Article
• Authors: Duan, Huiming; Min, Zijian; Yang, Jinchen
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 19:Number 2(2016)
• Page Start: 447
• Page End: 456
• Publication Date: 2016-03-03
• Subjects: Isomorphic -- Factorization -- Complete tripartite graph; 05C35 05C75 05C60; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2016.1191173
• Languages: English
• ISSNs: 0972-0529

Abstract

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 ).