1-Factorization of K 2n

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1-Factorization of K_{2n} --- один-факторизация графа K_{2n}.

A one-factorization of K_{2n} is a partition of the edge-set of K_{2n} into 2n-1 one-factors. A perfect one-factorization (P1F) is a one-factorization in which every pair of distinct one-factors forms a Hamiltonian cycle of K_{2n}. P1Fs of K_{2n} are known to exist when 2n-1 or n is prime, and for 2n
\in \{16, 28, 36,40, 50, 126, 170, 244, 344, 730, 1332, 1370, 1850,
2198, 3126, 6860, 12168, 16808, 29792\}.

It has been conjectured that a perfect one-factorization of K_{2n} exists for all n \geq 2.