Homogeneous factorisations of complete multipartite graphs Original Research Article

A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups image with image fixing each part of the partition setwise and image preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that image acts regularly on vertices. We provide a necessary and sufficient condition for the existence of such factorisations and produce many interesting examples. In particular we give a complete determination of the parameters for which homogeneous factorisations exist with image cyclic.