Laman graph

Summary

A Laman graph is a graph with $2n - 3$ edges on $n$ vertices in which no set of $k \ge 2$ vertices spans more than $2k - 3$ edges. These are exactly the graphs that are minimally rigid in the plane for generic positions of the vertices. So they reduce a question of rigidity of frameworks in the plane to a count of edges, which can be checked by efficient algorithms.