 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 "K"3,3.

 and define a graph as being formula_1-sparse if every nonempty subgraph with formula_2 vertices has at most formula_3 edges, and formula_1-tight if it is formula_1-sparse and has exactly formula_3 edges.Thus, in their notation, the Laman graphs are exactly the (2,3)-tight graphs, and the subgraphs of the Laman graphs are exactly the (2,3)-sparse graphs.