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; Danziger, Peter. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - 32:2(2016), pp. 521-531. [10.1007/s00373-015-1582-x]
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 allegati a questo prodotto
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