{
  "abstract": "In this short note, we obtain upper bounds on the chromatic numbers of spheres using recent improvements in bounds for Euclidean space. We show that $χ(S^n_{R}) \\leq (ξ_R + o(1))^n$, where $ξ_R = \\frac{3\\sqrt 3}{2}(1-1/(4R^2)) $ and $χ(S^n_R)$ denotes the chromatic number of the $n$-dimensional sphere of a fixed radius $R$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32408",
  "author_total": 3,
  "authors": [
    {
      "name": "A. I. Bikeev"
    },
    {
      "name": "V. A. Voronov"
    },
    {
      "name": "A. M. Raigorodskii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79kt0htdsh4s8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32408",
  "fulltext_url": null,
  "id": "79kt0htdsh4s8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32408",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223661679",
  "pdf_url": "https://arxiv.org/pdf/2610.32408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79kt0htdsh4s8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved upper bound on the chromatic number of the n-dimensional sphere",
  "title_text": "An improved upper bound on the chromatic number of the n-dimensional sphere",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/79kt0htdsh4s8",
  "venue": "arXiv",
  "versions": []
}