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Find a safe edge<br />
Proof: Let T be a MST that includes A<br />
� Case 1: (u, v) T => done.<br />
� Case 2: (u, v) not in T:<br />
� Exist edge (x, y) T cross the cut, (x, y) A<br />
� Removing (x, y) breaks T into two components.<br />
� Adding (u, v) reconnects 2 components<br />
� T´ = T - {(x, y)} {(u, v)} is a spanning tree<br />
� w(T´) = w(T) - w(x, y) + w(u, v) w(T) => T’ is a MST => done<br />
My T. Thai<br />
mythai@cise.ufl.edu<br />
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