The sharp K4-percolation threshold on the Erdős–Rényi random graph

Brett Kolesnik

doi:10.1214/21-EJP710

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Home > Journals > Electron. J. Probab. > Volume 27 > Article

2022 The sharp

{K_{4}}

-percolation threshold on the Erdős–Rényi random graph

Brett Kolesnik

Author Affiliations +

Brett Kolesnik¹
¹Department of Mathematics, University of California, San Diego

Electron. J. Probab. 27: 1-23 (2022). DOI: 10.1214/21-EJP710

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Abstract

We locate the critical threshold ${p_{c}}\sim 1/ \sqrt{3n\log n}$ at which it becomes likely that the complete graph ${K_{n}}$ can be obtained from the Erdős–Rényi graph ${\mathcal{G}_{n,p}}$ by iteratively completing copies of ${K_{4}}$ 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.

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Brett Kolesnik. "The sharp ${K_{4}}$ -percolation threshold on the Erdős–Rényi random graph." Electron. J. Probab. 27 1 - 23, 2022. https://doi.org/10.1214/21-EJP710