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Sharp threshold for rigidity of random graphs
Alan Lew, Eran Nevo, Yuval Peled, Orit E. Raz · 2022-02-21 · via math.PR updates on arXiv.org

We consider the Erdős-Rényi evolution of random graphs, where a new uniformly distributed edge is added to the graph in every step. For every fixed $d\ge 1$, we show that with high probability, the graph becomes rigid in $\mathbb R^d$ at the very moment its minimum degree becomes $d$, and it becomes globally rigid in $\mathbb R^d$ at the very moment its minimum degree becomes $d+1$.

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