Publication: Solutions to the Oberwolfach Problem for orders 18 to 40

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Title Solutions to the Oberwolfach Problem for orders 18 to 40
Authors/Editors* A. Deza, F. Franek, W. Hua, M. Meszka, A. Rosa
Where published* Advanced Optimization Laboratory Technical Reports
How published* Technical Report
Year* 2008
Pages 10
Keywords Oberwolfach solutions 2-factorizations pure mixed differences
The Oberwolfach problem (OP) asks whether the complete graph on n vertices (for n odd) or the complete graph less a perfect matching (for n even) admits a 2-factorization where each 2-factor is isomorphic to a given 2-factor, F. The order n and the type of the 2-factor F are the parameters of the problem. For n ≤ 17, the existence of a solution has been resolved for all possible parameters. There are also many special types of 2-factors for which solutions to OP are known. We provide solutions to OP for all orders n, 18 ≤ n ≤ 40. The computational results for higher orders were obtained using the SHARCNET high-performance computing cluster.
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