Cyclic and Dihedral 1-Factorizations of Multipartite Graphs

Abstract

An automorphism group $G$ of a $1$-factorization of the complete multipartite graph $K_{m\times n}$ consists of permutations of the vertices of the graph mapping factors to factors. In this paper, we give a complete answer to the existence problem of a $1$-factorization of $K_{m\times n}$ admitting a cyclic or dihedral group acting sharply transitively on the vertices of the graph.