I cut a number of eggs for a salad and had most yolks stuck to the knife. The problem, to me, is that the egg falls apart. The yolk is loose and the white as well.
Does anybody know a way to cut the egg without that happening?
Instead of using a chef's knife, cut it with a knife that has a thinner profile and a lower amount of surface area. This will decrease the amount of friction created as the blade slides through the yolk, and decrease the sticking. The wire cutters are able to do this because they have an extremely small area actually in contact with the yolk.
Try a boning knife, for example.