Abstract.
The Hamilton-Waterloo problem asks for a 2-factorisation of K v in which r of the 2-factors consist of cycles of lengths a 1,a 2,…,a t and the remaining s 2-factors consist of cycles of lengths b 1,b 2,…,b u (where necessarily ∑ i=1 t a i =∑ j=1 u b j =v). In this paper we consider the Hamilton-Waterloo problem in the case a i =m, 1≤i≤t and b j =n, 1≤j≤u. We obtain some general constructions, and apply these to obtain results for (m,n)∈{(4,6),(4,8),(4,16),(8,16),(3,5),(3,15),(5,15)}.
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Received: July 5, 2000
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Adams, P., Billington, E., Bryant, D. et al. On the Hamilton-Waterloo Problem. Graphs Comb 18, 31–51 (2002). https://doi.org/10.1007/s003730200001
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DOI: https://doi.org/10.1007/s003730200001