{
  "abstract": "Let $G(n,m)$ be the Erdos-Renyi random graph with $n$ vertices and $m$ edges and let $δ>0$. Alon and Krivelevich [Combinatorica 1997] proved that for any sequence $m\\leq n^{3/2-δ}$ there \\emph{exists} an integer sequence $q=q(n)$ such that the chromatic number of $G(n,m)$ equals either $q$ or $q+1$ with probability tending to one as $n\\to\\infty$. In this paper, we give an explicit formula for this sequence $q(n)$ and confirm their result under a less restrictive assumption that $m=o(n^{3/2})$. Furthermore, we show that for all but a vanishing proportion of the admissible values of $m$, the chromatic number of $G(n,m)$ equals $q$ with high probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33678",
  "author_total": 4,
  "authors": [
    {
      "name": "Amin Coja-Oghlan"
    },
    {
      "name": "Mikhail Isaev"
    },
    {
      "name": "Mihyun Kang"
    },
    {
      "name": "Pavel Zakharov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxbevprwj24bd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33678",
  "fulltext_url": null,
  "id": "dxbevprwj24bd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33678",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223816847",
  "pdf_url": "https://arxiv.org/pdf/2610.33678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxbevprwj24bd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The chromatic number of a random graph with $o(n^{3/2})$ edges",
  "title_text": "The chromatic number of a random graph with o(n^3/2) edges",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/dxbevprwj24bd",
  "venue": "arXiv",
  "versions": []
}