I think it should be false because there may be more than one edge with the same weight.

  • 3
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    – Raphael
    Aug 15 '18 at 17:46
  • $\begingroup$ You are on the right track. Try to construct a concrete example in which the algorithm may have different outputs. $\endgroup$
    – dave
    Aug 15 '18 at 21:22

Your are right. A simplest example would be a triangle with weight 1, 1, 1.

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