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

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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.

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Acknowledgments

M. Buratti is supported by MIUR (project “Disegni combinatori, grafi e loro applicazioni”, PRIN 2008). P. Danziger is supported by the NSERC Discovery program. The bulk of this work was carried out when the second author visited University Sapienza of Rome. The support and hospitality of the department during this visit was greatly appreciated.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123, Perugia, Italy

    Marco Buratti

  2. Department of Mathematics, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canada

    Peter Danziger

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  1. Marco Buratti
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  2. Peter Danziger
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Correspondence to Marco Buratti.

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Buratti, M., Danziger, P. A Cyclic Solution for an Infinite Class of Hamilton–Waterloo Problems. Graphs and Combinatorics 32, 521–531 (2016). https://doi.org/10.1007/s00373-015-1582-x

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  • DOI: https://doi.org/10.1007/s00373-015-1582-x

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