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{\bf Mariusz Meszka}
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{\bf $k$-Cycle Free One-Factorizations of Complete Graphs}
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It is proved that for every $n\geq 3$ and every even
$k\geq 4$, where $k\neq 2n$, there exists one-factorization of the
complete graph $K_{2n}$ such that any two one-factors do not
induce a graph with a cycle of length $k$ as a component.
Moreover, some infinite classes of one-factorizations, in which
lengths of cycles induced by any two one-factors satisfy a given
lower bound, are constructed.



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