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Hamiltonian decompositions of complete graphs. (English) Zbl 0542.05044
The paper presents a procedure for constructing all Hamiltonian decompositions of the complete graph $$K_{2n+1}$$. The technique is then applied to find a necessary and sufficient condition for a decomposition of the edge set of $$K_ r$$ ($$r\leq 2n)$$ into n classes, each class consisting of disjoint paths to be extendible to a Hamiltonian decomposition of $$K_{2n+1}$$ so that each of the classes forms part of a Hamilton cycle.
Reviewer: W.K.Chen

##### MSC:
 05C45 Eulerian and Hamiltonian graphs 05C38 Paths and cycles 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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##### References:
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