Sharp threshold for rigidity of random graphs

Alan Lew; Eran Nevo; Yuval Peled; Orit E. Raz

doi:10.1112/blms.12740

Sharp threshold for rigidity of random graphs

Alan Lew, Eran Nevo, Yuval Peled, Orit E. Raz

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 (Formula presented.), we show that with high probability, the graph becomes rigid in (Formula presented.) at the very moment its minimum degree becomes (Formula presented.), and it becomes globally rigid in (Formula presented.) at the very moment its minimum degree becomes (Formula presented.).

Original language	English
Pages (from-to)	490-501
Number of pages	12
Journal	Bulletin of the London Mathematical Society
Volume	55
Issue number	1
DOIs	https://doi.org/10.1112/blms.12740
State	Published - 1 Feb 2023
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1112/blms.12740

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AB - 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 (Formula presented.), we show that with high probability, the graph becomes rigid in (Formula presented.) at the very moment its minimum degree becomes (Formula presented.), and it becomes globally rigid in (Formula presented.) at the very moment its minimum degree becomes (Formula presented.).

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Sharp threshold for rigidity of random graphs

Abstract

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