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Cyclic one-factorization of the complete graph. (English) Zbl 0624.05051
Let $$K_ n$$ be the complete graph of order n with vertex set V and edge set E. A 1-factorization of $$K_ n$$ is a partition of E into n-1 one factors, so that each 1-factor is a partition of V. An automorphism of a 1-factorization is a permutation of V which maps 1-factors onto 1- factors. A 1-factorization is cyclic if it admits an n-cycle as an automorphism. In this paper the authors show that cyclic 1-factorizations exists if and only if n is even and $$n\neq 2^ t$$, $$t\geq 3$$. They also enumerate cyclic 1-factorizations of $$K_ n$$ for $$n\leq 16$$.
Reviewer: L.Caccetta

MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
Keywords:
1-factorization; automorphism
Full Text:
References:
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