Abstract
We present a simple, direct proof of Hwang's characterization of rectilinear Steiner minimal trees [3]: LetS be a set of at least five terminals in the plane. If no rectilinear Steiner minimal tree forS has a terminal of degree two or more, there is a tree in which at most one of the Steiner points does not lie on a straight linel, and the tree edges incident to the Steiner points onl appear on alternate sides. This theorem has been found useful in proving other results for rectilinear Steiner minimal trees.
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Richards, D.S., Salowe, J.S. A simple proof of Hwang's theorem for rectilinear Steiner minimal trees. Ann Oper Res 33, 549–556 (1991). https://doi.org/10.1007/BF02067241
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DOI: https://doi.org/10.1007/BF02067241