On bipartite 2‐factorizations of k n − I and the Oberwolfach problem

It is shown that if F 1 , F 2 , …, F t are bipartite 2‐regular graphs of order n and α 1 , α 2 , …, α t are positive integers such that α 1 + α 2 + ⋅ + α t = ( n − 2)/2, α 1 ≥3 is odd, and α i is even for i = 2, 3, …, t , then there exists a 2‐factorization of K n − I in which there are exactly α i 2‐factors isomorphic to F i for i = 1, 2, …, t . This result completes the solution of the Oberwolfach problem for bipartite 2‐factors. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:22‐37, 2011