A simple proof of Hwang’s theorem for rectilinear Steiner minimal trees

The authors present a simple, direct proof of Hwang’s characterization of rectilinear Steiner minimal trees: Let S be a set of at least five terminals in the plane. If no rectilinear Steiner minimal tree for S 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 line l, and the tree edges incident to the Steiner points on l appear on alternate sides. This theorem has been found useful in proving other results for rectilinear Steiner minimal trees.