The Hamilton–Waterloo Problem for Hamiltonian Cycles and Cm‐Factors

ABSTRACT The Hamilton‐Waterloo problem asks for the existence of a 2‐factorization of the complete graph of odd order in which of the 2‐factors are isomorphic to a given 2‐factor , and of the 2‐factors are isomorphic to a given 2‐factor , with . We provide a complete constructive solution to this problem in the case when 2‐factors are either Hamiltonian cycles or consist of ‐cycles only, where is odd and .