Let n be a positive integer. A Steiner tree associated with a finite set S of points in the Euclidean n-space is a finite collection T of straight-line segments in that space such that any two points in S are joined by a unique path in T , and its length is the sum of the segment lengths. Show that there exists a Steiner tree of length 1+(2n−1−1)3 associated with the vertex set of a unit n-cube.
combinatoricsSteiner Trees