Every $d(d+1)$-connected graph is globally rigid in $\mathbb{R}^d$

Soma Villányi

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arXiv · 2312.02028

Every $d(d+1)$-connected graph is globally rigid in $\mathbb{R}^d$

Soma Villányi

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Abstract

Using a probabilistic method, we prove that $d(d+1)$-connected graphs are rigid in $\mathbb{R}^d$, a conjecture of Lovász and Yemini. Then, using recent results on weakly globally linked pairs, we modify our argument to prove that $d(d+1)$-connected graphs are globally rigid, too, a conjecture of Connelly, Jordán and Whiteley. The constant $d(d+1)$ is best possible.

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BibTeX RIS

Soma Villányi. 2023-12-04. Every $d(d+1)$-connected graph is globally rigid in $\mathbb{R}^d$. https://arxiv.org/abs/2312.02028

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