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On the construction of odd cycle systems. (English) Zbl 0704.05031

Let \(K_ n\) be a complete nonoriented graph. A cycle system of order n is defined as a decomposition of the edge set of \(K_ n\) into disjoint cycles of the length k. The necessary conditions for \(K_ n\) to be decomposable into k-cycles are \(n\geq k,\) n is odd, \(2k| n(n-1).\) (*)
In the paper there is investigated the case of odd k. It is shown that necessary conditions (*) are also sufficient if and only if each admissible graph \(K_ n\) (satisfying (*) for \(k\leq n<3k)\) is decomposable into k-cycles. The cases of decompositions into 15-cycles and 21-cycles are solved completely.
Reviewer: L.Niepel

MSC:

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