{
  "abstract": "We give a nibble-free construction proving $R(3,k)\\ge(1/200+o(1))k^2/\\log k$. We also include Shearer's proof bounding the independence number of a triangle-free graph, which implies $R(3,k)\\le (1+o(1))(k^2/\\log k)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01782",
  "author_total": 5,
  "authors": [
    {
      "name": "Samuel Harris"
    },
    {
      "name": "Zion Hefty"
    },
    {
      "name": "Paul Horn"
    },
    {
      "name": "Dylan King"
    },
    {
      "name": "Florian Pfender"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxqtsh21tac6c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01782",
  "fulltext_url": null,
  "id": "bxqtsh21tac6c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01782",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7207808327",
  "pdf_url": "https://arxiv.org/pdf/2609.01782",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxqtsh21tac6c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01782",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A short proof that $R(3,k)=Θ(k^2/\\log k)$",
  "title_text": "A short proof that R(3,k)=Θ(k^2/log k)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/bxqtsh21tac6c",
  "venue": "arXiv",
  "versions": []
}