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Let $P$ be a set of points. The minimal triangulation of $P$ is a triangulation $T$ of the points in $P$ such that the total length of the edges in $T$ is the smallest possible amongst all possible triangulations of $P.$

I am looking for the smallest (and most concise) example such that the Delaunay triangulation of $P$ is not equal to the minimal triangulation of $P.$

Anyone happens to have a good example of this?

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up vote 7 down vote accepted

This picture shows an example of a Delaunay triangulation that is not a minimum weight triangulation. Since it uses only 4 points it is the smallest example.

enter image description here

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