We introduce the concept of a 2-starter in a group G 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.
On sharply vertex-transitive 2-factorizations of the complete graph / Buratti, Marco; Rinaldi, G.. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 111:(2005), pp. 245-256. [10.1016/j.jcta.2004.11.014]