On perfectly friendly bisections of random graphs
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Author(s)
Minzer, Dor
Sah, Ashwin
Sawhney, Mehtaab
Date Issued
November 2024
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Citation
Dor Minzer. Ashwin Sah. Mehtaab Sawhney. "On perfectly friendly bisections of random graphs." Ann. Probab. 52 (6) 2281 - 2341, November 2024.
Version
Final published version
Abstract
We prove that there exists a constant γ_crit≈0.17566such that if G∼G(nⓜ,1⁄2)ε>0with high probability G has a equipartition such that each vertex has (γ_crit-ε) √nmore neighbors in its own part than in the other part and with high probability no such partition exists for a separation of (γ_crit+ε) √n G(nⓜ,1⁄2).
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DOI of Published Version
https://doi.org/10.1214/24-aop1696
