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Hamilton decompositions of complete graphs with a 3-factor leave. (English) Zbl 1044.05058
Summary: We show that for any 2-factor $$U$$ of $$K_n$$ with $$n$$ even, there exists a 3-factor $$T$$ of $$K_n$$ such that $$E(U) \subset E(T)$$ so that $$K_n - E(T)$$ admits a Hamilton decomposition. This is proved with the method of amalgamations (graph homomorphisms), using a new result that concerns graph decompositions that are fairly divided, but not necessarily regular.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C45 Eulerian and Hamiltonian graphs
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##### References:
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