Hi, I wanted to know whether this is also a valid solution:
let e= (u,v). we create a cut C1 ({u}, G \ {U}). A= null is a promising set, and has no edges. therefore, this cut respects A.
All edges (u,y) are connecting the graph. if w(e) <= Min (w(u,y)) then e is a safe edge for A, and therefore there exists a MST T that contains e.
If not, check the same for cut C2 ({v}, G \ {v}) and return the result.
David