Connected rigidity matroids and unique realizations of graphs
type: Item
instance of: scholarly article
title: Connected rigidity matroids and unique realizations of graphs
zbMATH Open document ID: 1076.05021
author: Bill Jackson
author: Tibor Jordán
published in: Journal of Combinatorial Theory. Series B
publication date: 2005-05-04T00:00:00Z
review text: A graph is shown to have a unique realization in the plane if and only if it is 3-connected and redundantly rigid, resolving the last open case of a conjecture by \textit{B. Hendrickson} [SIAM J. Comput. 21, 65--84 (1992; Zbl 0756.05047)]. One key ingredient for the proof is the fact that 2-rigidity leads to a finer decomposition of the rigidity matroid than the one pointed out by \textit{B. Servatius} [SIAM J. Discrete Math. 2, 582--589 (1989; Zbl 0723.05034)], another is the new characterization of M-circuits by \textit{A. Berg} and \textit{T. Jordán} [J. Comb. Theory, Ser. B 88, 77--97 (2003; Zbl 1036.05047)].
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 2165067
zbMATH Keywords: generic rigidity
zbMATH Keywords: 2--rigidity
reviewed by: Herman J. Servatius
MaRDI profile type: Publication
full work available at URL: j.jctb.2004.11.002
OpenAlex ID: W2148291654
cites work: A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid.
cites work: Algorithms - ESA 2003
cites work: Rigidity and energy
cites work: Q3974964
cites work: Independence and port oracles for matroids, with an application to computational learning theory
cites work: Q5461825
cites work: Q4076414
cites work: Q4279195
cites work: Conditions for Unique Graph Realizations
cites work: The Molecule Problem: Exploiting Structure in Global Optimization
cites work: On graphs and rigidity of plane skeletal structures
cites work: On Generic Rigidity in the Plane
cites work: Q3135082
cites work: Birigidity in the Plane
cites work: Q3694165
cites work: Q5524326
cites work: Q4012027
cites work: Q4717849
DOI: 10.1016/J.JCTB.2004.11.002
description: scientific article; zbMATH DE number 2165067