{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05254",
  "author_total": 4,
  "authors": [
    {
      "name": "Bruno Baldissera"
    },
    {
      "name": "Gabriel Dias do Couto"
    },
    {
      "name": "Simon Griffiths"
    },
    {
      "name": "Luiz Moreira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmqx6rtj7kv51.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05254",
  "fulltext_url": null,
  "id": "dmqx6rtj7kv51",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05254",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05254",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmqx6rtj7kv51.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05254",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05254"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Connectivity Threshold for Friends and Strangers graphs",
  "title_text": "The Connectivity Threshold for Friends and Strangers graphs",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/dmqx6rtj7kv51",
  "venue": "arXiv",
  "versions": []
}