MathDB

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+(2^{n-1}-1)\sqrt{3}

associated with the vertex set of a unit

n

-cube.

Problem Statement