On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem

Bryant, Darryn and Danziger, Peter (2011) On bipartite 2-factorizations of K(n)-I and the Oberwolfach problem. Journal of Graph Theory, 681: 22-37. doi:10.1002/jgt.20538

It is shown that if F-1, F-2, ... , F-t are bipartite 2-regular graphs of order n and alpha(1), alpha(2),..., alpha(t) are positive integers such that alpha(1)+ alpha(2) + ... + alpha(t) = (n-2)/2, alpha(1)>= 3 is odd, and alpha(i) is even for i = 2, 3,..., t, then there exists a 2-factorization of K-n-I in which there are exactly alpha(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. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 22-37, 2011

Formatted abstract

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.