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arXiv · 2611.05254

The Connectivity Threshold for Friends and Strangers graphs

Bruno Baldissera·Gabriel Dias do Couto·Simon Griffiths·Luiz Moreira
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Abstract

The concept of the Friends and Strangers graph $FS(G,H)$ associated with two graphs $G$ and $H$ was recently introduced by Defant and Kravitz and has generated significant interest. In a companion article, joint with Alon, they consider the behaviour of $FS(G,H)$ in the case where $G$ and $H$ are Erdős-Rényi random graphs, and prove that the threshold for connectivity is of the form $n^{-1/2+o(1)}$. In this paper we prove that the threshold is $n^{-1/2}\sqrt{\log{n}}$, up to a multiplicative constant, answering a question from Alon, Defant and Kravitz.

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Bruno Baldissera, Gabriel Dias do Couto, Simon Griffiths, Luiz Moreira. 2026-11-03. The Connectivity Threshold for Friends and Strangers graphs. https://arxiv.org/abs/2611.05254

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