Smallest edge in a euclidean Steiner tree smaller than the smallest edge of the corresponding euclidean MST?

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Given a set of 2D points V in a plane, consider the euclidean minimum steiner tree S, and the euclidean minimum spanning tree M on V. Let s be the length of the smallest length edge in S, and m be the smallest length edge in M. Is s <= m? If yes, How can I prove it?

asked 23 secs ago

Aman Singh

58

Smallest edge in a euclidean Steiner tree smaller than the smallest edge of the corresponding euclidean MST?