{
  "abstract": "Coloring a graph G consists in finding an assignment of colors c : V (G) → {1, . . . , p} such that any pair of adjacent vertices receives different colors. The minimum integer p such that a coloring exists is called the chromatic number of G, denoted by χ(G). We investigate the chromatic number of powers of graphs, i.e. the graphs obtained from a graph G by adding an edge between every pair of vertices at distance at most k. For k = 1, Brooks' theorem states that every connected graph of maximum degree ∆ 3 except the clique on ∆ + 1 vertices can be colored using ∆ colors (i.e. one color less than the naive upper bound). For k 2, a similar result holds: except for Moore graphs, the naive upper bound can be lowered by 2. We prove that for k 3 and for every ∆, we can actually spare k -2 colors, except for a finite number of graphs. We then improve this value to Θ((∆ -1) k 12 ).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Théo Pierron"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmmenyveznfbb.bib",
  "cited_by": 0,
  "doi": "10.1016/j.ejc.2023.103822",
  "fulltext_url": null,
  "id": "dmmenyveznfbb",
  "issns": [
    "0195-6698",
    "1095-9971"
  ],
  "landing_url": "https://hal.science/hal-05745804v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
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      "hal",
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    ],
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    [
      "openalex",
      "1703|Advanced Graph Theory Research"
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  "openalex": "W2981171106",
  "pdf_url": "https://hal.science/hal-05745804/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/dmmenyveznfbb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:33Z",
      "native_id": "hal-05745804",
      "source": "hal",
      "url": "https://hal.science/hal-05745804v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Brooks-like result for graph powers $",
  "title_text": "A Brooks-like result for graph powers $",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:33Z",
  "url": "https://research.draconitic.com/paper/dmmenyveznfbb",
  "venue": "European Journal of Combinatorics",
  "versions": []
}