The Hamilton-Waterloo Problem: The Case Of Hamilton Cycles And 4-cycles

The Hamilton-Waterloo problem is to determine the existence of a 2-factorization of K_n or K_n- I in which r of the 2-factors are isomorphic to a given 2-factor Q and s of the 2-factors are isomorphic to a given 2-factor R. In this paper we consider the case when Q is a Hamilton cycle and R is a 4-cycle. We solve the problem completely with n = 16k,r = 0,1,...,8 k- 1 and mostly with n = 16 k + 4,16 k + 8,16 k+ 12.