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A 2-factorization {F1, F2,…,Fd} of a 2d-regular graph G such that each [Formula: see text] and the remaining Fi's are all Hamilton cycles is called Hamilton cycle rich 2-factorization of G, where Gi's are the given non-isomorphic 2-factors of G. In this paper, we prove that there exists a 2-factorization {F1, F2,…,Fn} of K2n,2n such that F1 ≅ G1, F2 ≅ G2 and the remaining Fi's are Hamilton cycles of K2n,2n, where G1 and G2 are the given two non-isomorphic 2-factors of K2n,2n. In fact our result together with the earlier results settles the existence of Hamilton cycle rich 2-factorizations of K(m, p), the complete p-partite graph with m vertices in each partite set, except when (m, p) = (2n + 1, 2), in the case that two of the 2-factors are isomorphic to the given two non-isomorphic 2-factors and the remaining are Hamilton cycles.

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