English

Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs

Combinatorics 2023-07-13 v1

Abstract

In this paper we consider the class of graphs which are redundantly dd-rigid and (d+1)(d+1)-connected but not globally dd-rigid, where dd is the dimension. This class arises from counterexamples to a conjecture by Bruce Hendrickson. It seems that there are relatively few graphs in this class for a given number of vertices. Using computations we show that K5,5K_{5,5} is indeed the smallest counterexample to the conjecture.

Keywords

Cite

@article{arxiv.2212.11818,
  title  = {Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs},
  author = {Georg Grasegger},
  journal= {arXiv preprint arXiv:2212.11818},
  year   = {2023}
}

Comments

7 pages, 2 figures

R2 v1 2026-06-28T07:49:07.137Z