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2022 The sharp K4-percolation threshold on the Erdős–Rényi random graph
Brett Kolesnik
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Electron. J. Probab. 27: 1-23 (2022). DOI: 10.1214/21-EJP710

Abstract

We locate the critical threshold pc13nlogn at which it becomes likely that the complete graph Kn can be obtained from the Erdős–Rényi graph Gn,p by iteratively completing copies of K4 minus an edge. This refines work of Balogh, Bollobás and Morris that bounds the threshold up to multiplicative constants.

Acknowledgments

The author gratefully acknowledges the financial support of NSERC of Canada, and thanks Omer Angel for many helpful discussions.

Citation

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Brett Kolesnik. "The sharp K4-percolation threshold on the Erdős–Rényi random graph." Electron. J. Probab. 27 1 - 23, 2022. https://doi.org/10.1214/21-EJP710

Information

Received: 22 February 2021; Accepted: 27 September 2021; Published: 2022
First available in Project Euclid: 26 January 2022

Digital Object Identifier: 10.1214/21-EJP710

Subjects:
Primary: 05C80 , 60K35

Keywords: Bootstrap percolation , random graph , triadic closure , weak saturation

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