On sharply vertex transitive 2-factorizations of the complete graph

We introduce the concept of a 2-starter in a groupG of odd order.We prove that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G. Some classes of 2-starters are studied, with special attention given to those leading to solutions of some Oberwolfach or Hamilton–Waterloo problems. © 2005 Elsevier Inc. All rights reserved.