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  "body": "\n## Summary\n\nA Laman graph is a [[graph|00C0BR7D7H]] with $2n - 3$ edges on $n$ vertices in which no set of $k \\ge 2$ vertices spans more than $2k - 3$ edges.\nThese are exactly the graphs that are minimally rigid in the plane for generic positions of the vertices.\nSo they reduce a question of [[rigidity of frameworks|V5YS9BZX0N]] in the plane to a count of edges, which can be checked by efficient algorithms.\n\n## Explanations\n\n### L1 human\n\nA point in the plane has two degrees of freedom, and a rigid shape in the plane can still slide and turn in three ways.\nSo $n$ points need $2n - 3$ bars to be held rigid, and no part may waste bars on a piece that is already rigid.\nA triangle has $3$ vertices and $3 = 2 \\cdot 3 - 3$ edges, and it is a Laman graph.\nThe complete graph on $4$ vertices has $6 \u003e 5$ edges, so it has one bar too many.\n",
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