{
  "abstract": "We show that optimally pseudorandom $K_4$-free graphs of order $n$ and degree $d = Θ(n^{4/5})$ exist by constructing a graph in the split Cayley hexagon, matching the known upper bound. This resolves the first open case for $K_k$-free graphs after $k=3$ for which Alon gave a tight construction in 1994. This has a variety of implications for $K_4$-free pseudorandom graphs. Furthermore, it implies an explicit lower bound on the Ramsey number of $r(4, t) \\geq t^{1.\\overline{6} - o(1)}$, improving the previous record by Kostochka, Pudlák, and Rödl of $r(4, t) \\geq t^{1.6-o(1)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32461",
  "author_total": 3,
  "authors": [
    {
      "name": "Jie Han"
    },
    {
      "name": "Ferdinand Ihringer"
    },
    {
      "name": "Hendrik Van Maldeghem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xhhjkg9t08ed.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32461",
  "fulltext_url": null,
  "id": "9xhhjkg9t08ed",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32461",
  "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": "W7214733656",
  "pdf_url": "https://arxiv.org/pdf/2609.32461",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xhhjkg9t08ed.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32461",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32461"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Optimally pseudorandom $K_4$-free graphs",
  "title_text": "Optimally pseudorandom K_4-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/9xhhjkg9t08ed",
  "venue": "arXiv",
  "versions": []
}