Are you sure? I am fairly certain I have seen carriers work effectively even with 2000 fighters in the region.
It depends on the size of the naval region. A large region can require up to 4000 fighters to get max cover and give -100% efficiency for enemy carrier planes, while in a small one 500 might be enough.
The fighters also have to be using air superiority mission, interception won't work for air superiority.
100% enemy air superiority gives a 100% penalty meaning that your carriers are completely useless.
From what I have seen both cover and superiority is needed. You can't deny enemy Carriers with a single fighter plane, even if it can get 100% superiority without enemy planes present.