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Given points in Euclidean space of arbitrary dimension, we prove that thereexists a spanning tree having no vertices of degree greater than 3 with weightat most 1.559 times the weight of the minimum spanning tree. We also prove thatthere is a set of points such that no spanning tree of maximal degree 3 existsthat has this ratio be less than 1.447. Our central result is based on theproof of the following claim:  Given $n$ points in Euclidean space with one special point $V$, there existsa Hamiltonian path with an endpoint at $V$ that is at most 1.559 times longerthan 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 theminimal spanning tree.

On Improved Bounds on Bounded Degree Spanning Trees for Points in Arbitrary Dimension