On bipartite 2-factorizations of kn - I and the Oberwolfach problem

Abstract

It is shown that if F1, F2, a⋯, Ft are bipartite 2-regular graphs of order n and α1, α2, a⋯, αt are positive integers such that α1 + α2 + â + αt = (n - 2)/2, α1a ≥ 3 is odd, and αi is even for i = 2, 3, a⋯, t, then there exists a 2-factorization of Kn - I in which there are exactly αi 2-factors isomorphic to Fi for i = 1, 2, a⋯, t. This result completes the solution of the Oberwolfach problem for bipartite 2-factors. © 2010 Wiley Periodicals, Inc.