One-factorizations of complete graphs with vertex-regular automorphism groups

Abstract

We consider one-factorizations of K2n possessing an automorphism group acting regularly (sharply transitively) on vertices. We present some upper bounds on the number of one-factors which are fixed by the group; further information is obtained when equality holds in these bounds. The case where the group is dihedral is studied in some detail, with some non-existence statements in case the number of fixed one-factors is as large as possible. Constructions both for dihedral groups and for some classes of abelian groups are given. © 2002 John Wiley & Sons, Inc.