Further decompositions of complete tripartite graphs into 5-cycles Original Research Article

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r⩽s⩽t. Necessary and sufficient conditions are given for decomposability of K(r,s,t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirzakhani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235–241) and Cavenagh and Billington (J. Combin. 22 (2000) 41).