Planarity
A pointed pseudotriangulation is a planar straight-line drawing of a graph, with the properties that the outer face is convex, that every bounded face is a pseudotriangle, a polygon with only three convex vertices, and that the edges incident to every vertex span an angle of less than 180 degrees. The graphs that can be drawn as pointed pseudotriangulations are exactly the planar Laman graphs. However, Laman graphs have planar embeddings that are not pseudotriangulations, and there are Laman graphs that are not planar, such as the utility graph K3,3.
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