{
  "abstract": "Let $ζ$ be Euclidean norm of the degree sequence of a graph normalized by the graph size. We prove that when the vertices of a graph are randomly colored with $s$ colors such that the fraction of vertices in each color class is bounded away from zero, only two asymptotic regimes emerge. If $ζ=o(1)$, then the sizes of the subgraphs induced by the color classes concentrate around their expected values. If $ζ=Θ(1)$, then concentration depends on the color balance: for colorings with persisting imbalance, the total number $M$ of monochromatic edges stays bounded away from its mean with positive probability; otherwise, for vanishing imbalance, $M$ still concentrates. The same dichotomy holds for a broad class of randomly colored random graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02678",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicola Apollonio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37hm7symf46eg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02678",
  "fulltext_url": null,
  "id": "37hm7symf46eg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02678",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7160293552",
  "pdf_url": "https://arxiv.org/pdf/2605.02678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37hm7symf46eg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2605.02678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A universal dichotomy for concentration in randomly colored graphs",
  "title_text": "A universal dichotomy for concentration in randomly colored graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/37hm7symf46eg",
  "venue": "arXiv",
  "versions": []
}