# The number of realizations of a Laman graph

arXiv: https://arxiv.org/abs/1701.05500 · HTML: https://mlsanity.com/paper/1701.05500/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Learning Minimally Rigid Graphs with High Realization Counts](https://mlsanity.com/paper/2605.12427/) (2026)

## Abstract (arXiv)

Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursive formula for the number of complex solutions of such systems.