I never really have a problem when it comes to cut eggs for deviled eggs. The whites usually present no problem to cutting. Usually it is the yolk that sticks or breaks up, but since you are making deviled eggs that really doesn't matter since you mix up the yolk anyway. Cutting beautiful halves and quarters for other uses though can present a problem. Make sure you use a thin bladed knife, and stay away from serrated knives as that will tend to rip the yolk up. Dental floss works great, as Peachcreek mentioned, and if you have to do a lot of slicing (as cheesy as this sounds) one of those old-fashioned egg slicers works great (you know the one, where the egg rests in a cradle and a handle with 7 or 8 wires cut the egg.