Просмотр кода страницы 1-Factorization of K 2n

'''1-Factorization of <math>K_{2n}</math>''' --- один-факторизация графа
<math>K_{2n}</math>. 

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

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