On the domatic number of the n-cube and a conjecture of Zelinka (French)

Recently Zelinka [6] proved that d ( Q n ), the domatic number of the n -cube, is for n equal 2 p − 1 or n equal 2 p , exactly 2 p . We show here how d ( Q n ) can be determined for the preceding values, in a very simple way. We then disprove a conjecture by Zelinka and replace it by another closely related to a former one, involving the domination number of the n -cube.