The main result of this paper is the explicit construction, for any positive integer n, of a cyclic two-factorization of $K_{50n+5}$ with 20n+2 two-factors consisting of five (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.
A cyclic solution for an infinite class of Hamilton-Waterloo problems
BURATTI, Marco
;
2016
Abstract
The main result of this paper is the explicit construction, for any positive integer n, of a cyclic two-factorization of $K_{50n+5}$ with 20n+2 two-factors consisting of five (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.File in questo prodotto:
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