Homogeneous factorisations of complete multipartite graphs
- Giudici, Michael
- Li, Cai Heng
- Potočnik, Primož
- Praeger, Cheryl E.
Publication date
February 2007
DOI Publisher
Elsevier B.V. ISSN
0012-365X Citation count (estimate)
14Abstract
AbstractA homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M<G⩽Aut(Γ) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M 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 M cyclic
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