  Given points in Euclidean space of arbitrary dimension, we prove that there
exists a spanning tree having no vertices of degree greater than 3 with weight
at most 1.559 times the weight of the minimum spanning tree. We also prove that
there is a set of points such that no spanning tree of maximal degree 3 exists
that has this ratio be less than 1.447. Our central result is based on the
proof of the following claim:
  Given $n$ points in Euclidean space with one special point $V$, there exists
a Hamiltonian path with an endpoint at $V$ that is at most 1.559 times longer
than the sum of the distances of the points to $V$.
  These proofs also lead to a way to find the tree in linear time given the
minimal spanning tree.
