Multipartite graph decomposition: cycles and closed trails

Abstract

This paper surveys results on cycle decompositions of complete multipartite graphs (where the parts are not all of size 1, so the graph is not K_n ), in the case that the cycle lengths are “small”. Cycles up to length n are considered, when the complete multipartite graph has n parts, but not hamilton cycles. Properties which the decompositions may have, such as being gregarious, are also mentioned.