It is a wellknown fact of computational geometry that the edges of Minimum-weight Spanning Tree are also found in the Delaunay Triangulation of a planar pointset $\mathcal{P}$, i.e. $\operatorname{card}_E(\mathrm{MST(\mathcal{P})}\cap\mathrm{DT(\mathcal{P})}) = n-1$, where $\operatorname{card}_E$ denotes the cardinality of the edgeset.
Question:
is a similar result known for the Minimum Weight Triangulation, ie. what is known about $$\operatorname{card}_E(\mathrm{MST(\mathcal{P})}\cap\mathrm{MWT(\mathcal{P})})$$
