# Counting realizations of Laman graphs on the sphere

## TL;DR

This paper introduces an algorithm to count the number of ways a Laman graph can be realized on a sphere, using algebraic geometry tools related to moduli spaces of stable curves.

## Contribution

It provides a novel algorithm leveraging moduli space theory and Chow ring descriptions to count Laman graph realizations on the sphere.

## Key findings

- Algorithm computes realizations for general angles
- Utilizes moduli space of stable curves
- Connects graph realizations with algebraic geometry

## Abstract

We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space.