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Abelian 1-factorizations of the complete graph. (English) Zbl 0980.05039

The author considers the problem for which groups \(G\) there exists a \(1\)-factorization of the complete graph admitting \(G\) as a sharply-vertex-transitive automorphism group. He settles the problem for abelian groups by proving that any abelian group of even order that is not a cyclic 2-group is a solution of this problem. This way he extends a result by A. Hartman and A. Rosa [Eur. J. Comb. 6, 45-48 (1985; Zbl 0624.05051)].

MSC:

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

Citations:

Zbl 0624.05051
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References:

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[8] Korchmaros, G., Sharply Transitive 1-factorizations of the complete graph with an invariant 1-factor, J. Comb. Des., 2, 185-196 (1994) · Zbl 0856.05077
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