On universally rigid frameworks on the line

Authors

  • Tibor Jordan Departement of Operations Research, Eotvos University, Budapest
  • Viet Hang Nguyen Laboratoire G-SCOP, Grenoble UJF

DOI:

https://doi.org/10.11575/cdm.v10i2.62228

Keywords:

Universal rigidity, bar-and-joint framework, cover graph, generic rigidity, global rigidity, bipartite framework

Abstract

A d-dimensional bar-and-joint framework (G,p) with underlying graph G is called universally rigid if all realizations of G with the same edge lengths, in all dimensions, are congruent to (G,p). We give a complete characterization of universally rigid one-dimensional bar-and-joint frameworks in general position with a complete bipartite underlying graph. We show that the only bipartite graph for which all generic d-dimensional realizations are universally rigid is the complete graph on two vertices, for all d1. We also discuss several open questions concerning generically universally rigid graphs and the universal rigidity of general frameworks on the line. 

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Published

2016-04-28

Issue

Section

Articles