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* If ''n'' is odd and ''k'' ≥ ''n'', then ''G'' is 1-factorable. If ''n'' is even and ''k'' ≥ ''n'' − 1 then ''G'' is 1-factorable.
The [[overfull conjecture]] implies the 1-factorization conjecture.
The conjecture was confirmed by Csaba, Kühn, Lo, Osthus and Treglown for sufficiently large ''n''.
<ref {{Citation
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