{
  "abstract": "In 1992, Łuczak, Ruciński and Voigt showed that for any graph $H$, a parameter $m_1(H)$ - called the 1-density - governs the threshold at which the binomial random graph $G(n,p)$ inherits the vertex-Ramsey property. In 2000, Friedgut and Krivelevich showed this threshold is sharp for graphs satisfying a natural balancedness condition. In 1996, Kreuter showed that for any graphs $H_1, \\ldots, H_r$ with $m_1(H_1) \\geq \\cdots \\geq m_1(H_r)$, a parameter dependent only on $H_1$ and $H_2$ governs the threshold at which $G(n,p)$ inherits the `asymmetric' vertex-Ramsey property. We prove this threshold is sharp for graphs respecting natural balancedness conditions, including in the analogous hypergraph setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32677",
  "author_total": 3,
  "authors": [
    {
      "name": "Robert Hancock"
    },
    {
      "name": "Joseph Hyde"
    },
    {
      "name": "Mael Kupperschmitt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q9bq9dz9kv0y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32677",
  "fulltext_url": null,
  "id": "7q9bq9dz9kv0y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32677",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223701532",
  "pdf_url": "https://arxiv.org/pdf/2610.32677",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q9bq9dz9kv0y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32677",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32677"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharp asymmetric vertex-Ramsey properties of graphs",
  "title_text": "Sharp asymmetric vertex-Ramsey properties of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7q9bq9dz9kv0y",
  "venue": "arXiv",
  "versions": []
}