vertice foloving a texture - HOW?!

this is the situation. i have a sphere and i made a hole in it. the hole is not quite rounded so i want to move some vertices to make the hole more round shaped. when i move a vertice i lose that perfect sphere position and my hole is all grunged on the edges. not to much but it is never perfect.
my question is - is there a way i can move a vertice on, let’s say, x and that it automaticly moves on a y and z following the face of a sphere?

thanks

You can set your cursor to the center of the sphere and then rotate your points around that center.

Select the edges of you hole and Shift+S>Cursor to selection and To Sphere>100% (Ctrl+Shift+S, 100). Then Shift+C to relocate your cursor to the centre of the sphere and To Sphere again to make the sphere pereftly round.