  We consider partitions of a point set into two parts, and the lengths of the
minimum spanning trees of the original set and of the two parts. If $w(P)$
denotes the length of a minimum spanning tree of $P$, we show that every set
$P$ of $n \geq 12$ points admits a bipartition $P= R \cup B$ for which the
ratio $\frac{w(R)+w(B)}{w(P)}$ is strictly larger than $1$; and that $1$ is the
largest number with this property. Furthermore, we provide a very fast
algorithm that computes such a bipartition in $O(1)$ time and one that computes
the corresponding ratio in $O(n \log{n})$ time. In certain settings, a ratio
larger than $1$ can be expected and sometimes guaranteed. For example, if $P$
is a set of $n$ random points uniformly distributed in $[0,1]^2$ ($n \to
\infty$), then for any $\eps>0$, the above ratio in a maximizing partition is
at least $\sqrt2 -\eps$ with probability tending to $1$. As another example, if
$P$ is a set of $n$ points with spread at most $\alpha \sqrt{n}$, for some
constant $\alpha>0$, then the aforementioned ratio in a maximizing partition is
$1 + \Omega(\alpha^{-2})$. All our results and techniques are extendable to
higher dimensions.
