Decomposition of Complete Tri-Partite Graphs into 5-Cycles

Abstract

E. S. Mahmoodian gave necessary conditions for when the edges of a complete tripartite graph can be partitioned so that each set in the partition induces a 5-cycle. Since then, he, N. J. Cavenagh, E. J. Billington, S. Alipour, and E. Mollaahmadi have found several cases where these necessary conditions are also sufficient. We continue this investigation by considering further cases for complete tripartite graphs.