{
  "abstract": "We study the list chromatic number of generalized Johnson graphs. Recall that the vertices of such graphs are all possible $r$-element subsets of $[n] = \\{1, \\dotsc, n\\}$ and an edge is drawn between two vertices if and only if corresponding sets have exactly $s$ common elements. We prove that for any fixed $s \\geq 1$ and $r \\geq 2s + 2$ we have $χ_L(G(n,r,s)) = Θ(n^{s+1}\\ln n)$. In case where $s = 0$ we prove that for all $4\\ln n \\leq r \\leq n/20$ we have $χ_L(G(n,r,0)) \\geq \\frac{n}{120}\\ln\\left(\\frac{en}{r}\\right)$. Together with previous results of Bulankina, Inozemtsev and Kupavskii this proves that $χ_L(G(n,r,0)) = Θ\\left(n\\ln\\left(\\frac{en}{r}\\right)\\right)$ uniformly for $2 \\leq r \\leq (1/2-\\varepsilon)n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13723",
  "author_total": 1,
  "authors": [
    {
      "name": "M. Koshelev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77aptpjbyx738.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13723",
  "fulltext_url": null,
  "id": "77aptpjbyx738",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13723",
  "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": "W7221515076",
  "pdf_url": "https://arxiv.org/pdf/2610.13723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77aptpjbyx738.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.13723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "List chromatic number of $G(n,r,s)$ graphs",
  "title_text": "List chromatic number of G(n,r,s) graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/77aptpjbyx738",
  "venue": "arXiv",
  "versions": []
}