Realizations of Rigid Graphs
Computational Geometry
2022-01-04 v1
Abstract
A minimally rigid graph, also called Laman graph, models a planar framework which is rigid for a general choice of distances between its vertices. In other words, there are finitely many ways, up to isometries, to realize such a graph in the plane. Using ideas from algebraic and tropical geometry, we derive a recursive formula for the number of such realizations. Combining computational results with the construction of new rigid graphs via gluing techniques, we can give a new lower bound on the maximal possible number of realizations for graphs with a given number of vertices.
Cite
@article{arxiv.2201.00533,
title = {Realizations of Rigid Graphs},
author = {Christoph Koutschan},
journal= {arXiv preprint arXiv:2201.00533},
year = {2022}
}
Comments
In Proceedings ADG 2021, arXiv:2112.14770