{
  "abstract": "A graph is even-degenerate if we can order its vertices as $v_1,\\dots,v_n$ so that the number of edges from $v_i$ to $v_1,\\dots,v_{i-1}$ is even for all $i>2$. We show that the probability $G(n,p)$ is even-degenerate is $e^{-Ω(n/\\log\\log n)}$, which is only a factor of $\\log\\log n$ away, in the exponent, from the trivial lower bound $2^{-O(n)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03444",
  "author_total": 2,
  "authors": [
    {
      "name": "Ting-Wei Chao"
    },
    {
      "name": "Bruce Reed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ggmw8f8ehjjq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03444",
  "fulltext_url": null,
  "id": "0ggmw8f8ehjjq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03444",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ggmw8f8ehjjq.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A nearly tight bound on the probability $G(n,p)$ is even-degenerate",
  "title_text": "A nearly tight bound on the probability G(n,p) is even-degenerate",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/0ggmw8f8ehjjq",
  "venue": "arXiv",
  "versions": []
}