{
  "abstract": "It is shown that there exists $c > 0$ so that the Cayley graph over any finite abelian group $Z$ generated by $c \\log |Z|$ random elements is properly 3-colorable with high probability (as $|Z| \\to \\infty$). This is asymptotically tight and improves the best-known bound due to Alon of $\\frac{1}{4}\\log \\log |Z|$ elements. It also settles the abelian case of Alon's suggestion that a bound of $c \\log |G|$ may hold for any finite solvable group $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23762",
  "author_total": 1,
  "authors": [
    {
      "name": "Nathan Tung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fydk883fzc5rd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23762",
  "fulltext_url": null,
  "id": "fydk883fzc5rd",
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  "landing_url": "https://arxiv.org/abs/2606.23762",
  "language": null,
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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      "arxiv",
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      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7165803338",
  "pdf_url": "https://arxiv.org/pdf/2606.23762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fydk883fzc5rd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2606.23762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Coloring sparse random Cayley graphs",
  "title_text": "Coloring sparse random Cayley graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/fydk883fzc5rd",
  "venue": "arXiv",
  "versions": []
}