{
  "abstract": "An additive coloring assigns positive integer labels to the vertices of a graph so that adjacent vertices have different sums of their neighbors' labels. The additive chromatic number $η(G)$ is the least $k$ for which labels from $[k]$ suffice. We give an elementary orientation argument proving that every finite simple graph $G$ satisfies $η(G) \\leq Δ(G) + 1$. This argument yields a $(Δ(G) + 1)$-additive-coloring in polynomial time and improves upon the current best bound of $η(G) \\leq Δ(G)^{2} - Δ(G) + 1$, valid for $Δ(G) \\geq 2$, from Akbari, Ghanbari, Manaviyat, and Zare.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30174",
  "author_total": 2,
  "authors": [
    {
      "name": "Alex Koutsoutis"
    },
    {
      "name": "Joseph Koutsoutis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edg9m95q6q7rc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30174",
  "fulltext_url": null,
  "id": "edg9m95q6q7rc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30174",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.30174",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edg9m95q6q7rc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30174",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30174"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An elementary proof of a tight $Δ+1$ bound for the additive chromatic number",
  "title_text": "An elementary proof of a tight Δ+1 bound for the additive chromatic number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/edg9m95q6q7rc",
  "venue": "arXiv",
  "versions": []
}