On the Hamilton-Waterloo Problem for Bipartite 2-Factors


  • Contract grant sponsor: Australian Research Council's Discovery Projects funding scheme; Contract grant numbers: DP0770400 and DP0662946; Contract grant sponsor: Canadian Government National Science and Engineering Council.


Given two 2-regular graphs F1 and F2, both of order n, the Hamilton-Waterloo Problem for F1 and F2 asks for a factorization of the complete graph math formula into α1 copies of F1, α2 copies of F2, and a 1-factor if n is even, for all nonnegative integers α1 and α2 satisfying math formula. We settle the Hamilton-Waterloo Problem for all bipartite 2-regular graphs F1 and F2 where F1 can be obtained from F2 by replacing each cycle with a bipartite 2-regular graph of the same order.