http://lists.canonical.org/pipermail/kragen-tol/1999-July/000436.html

from that page: (some problem with voronoi diagram)

minimal spanning trees and Delaunay triangulations
Kragen Sitaker kragen@pobox.com
Thu, 8 Jul 1999 16:35:25 -0400 (EDT)

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This is probably a well-known result, or maybe it's just wrong, but I
was excited when I discovered it this morning.

It seems that every geometric minimal spanning tree of a set of points
must be a subgraph of every Delaunay triangulation of that set of points.