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The Hamilton-Waterloo problem for cycle sizes 3 and 4. (English) Zbl 1222.05119

Summary: The Hamilton-Waterloo problem seeks a resolvable decomposition of the complete graph \(K_n\), or the complete graph minus a 1-factor as appropriate, into cycles such that each resolution class contains only cycles of specified sizes. We completely solve the case in which the resolution classes are either all 3-cycles or 4-cycles, with a few possible exceptions when \(n=24\) and 48.

MSC:

05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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