{
  "abstract": "We consider a random subgraph G_p(n,r,<s) of the complete distance graph G(n,r,<s) whose vertices are the r-element subsets of the set {1,...,n} and whose edges join pairs of subsets that intersect in fewer than s elements; each edge survives independently of the others with probability p. The stability of the Erdos-Ko-Rado theorem is the event that the independence number of the random subgraph equals that of the original graph, N = C_{n-s}^{r-s}. For fixed r and s, two-sided bounds for the critical probability, whose ratio depends on r and s, were obtained by P. A. Ogarok and A. M. Raigorodskii. In this paper we establish the order of the critical probability for growing r=r(n) and s=s(n): if min{C_r^s r^2, s r^3} = o(n), then the upper and lower bounds differ only by an absolute constant factor. The proof is elementary; only one of the two branches of the growth condition uses the complete nontrivial-intersection theorem of Ahlswede-Khachatrian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16955",
  "author_total": 2,
  "authors": [
    {
      "name": "Vsevolod A. Pokhachevskiy"
    },
    {
      "name": "Andrei Raigorodskii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pypfkzv4zp3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16955",
  "fulltext_url": null,
  "id": "2pypfkzv4zp3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16955",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221809599",
  "pdf_url": "https://arxiv.org/pdf/2610.16955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2pypfkzv4zp3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16955"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the Stability of the Independence Number of the Distance Graph G(n,r,<s) for Growing r and s",
  "title_text": "On the Stability of the Independence Number of the Distance Graph G(n,r,<s) for Growing r and s",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/2pypfkzv4zp3b",
  "venue": "arXiv",
  "versions": []
}