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Hamilton decompositions of complete multipartite graphs with any 2-factor leave. (English) Zbl 1031.05108
Summary: For $$m \geq 1$$ and $$p \geq 2$$, given a set of integers $$s_1,\dots ,s_q$$ with $$s_j \geq p+1$$ for $$1 \leq j \leq q$$ and $$\Sigma_{j=1}^q s_j=mp$$, necessary and sufficient conditions are found for the existence of a Hamilton decomposition of the complete $$p$$-partite graph $$K_{m,\dots ,m}-E(U)$$, where $$U$$ is a 2-factor of $$K_{m,\dots ,m}$$ consisting of $$q$$ cycles, the $$j$$th cycle having length $$s_j$$. This result is then used to completely solve the problem when $$p = 3$$, removing the condition that $$s_j \geq p+1$$.

##### 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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