Mixed Volume Techniques for Embeddings of Laman Graphs
Combinatorics
2009-03-13 v2
Abstract
Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the viewpoint of Bernstein's Theorem. The focus of the paper is to provide the methods to study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. While in most cases the resulting bounds are weaker than the best known bounds on the number of embeddings, for some classes of graphs the bounds are tight.
Cite
@article{arxiv.0805.4120,
title = {Mixed Volume Techniques for Embeddings of Laman Graphs},
author = {Reinhard Steffens and Thorsten Theobald},
journal= {arXiv preprint arXiv:0805.4120},
year = {2009}
}
Comments
Thorough revision of the first version. (13 pages, 4 figures)