A Cyclic Solution for an Infinite Class of Hamilton–Waterloo Problems

The main result of this paper is the explicit construction, for any positive integer n, of a cyclic two-factorization of $$K_{50n+5}$$K50n+5 with $$20n+2$$20n+2 two-factors consisting of five $$(10n+1)$$(10n+1)-cycles and each of the remaining two-factors consisting of all pentagons. Then, applying suitable composition constructions, we obtain a few other two-factorizations also having two-factors of two distinct types.

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