{
  "abstract": "We prove that every $(P_2\\cup P_3)$-free graph $G$, with $k=ω(G)$, satisfies \\[ χ(G)=O\\!\\left(k^3\\frac{\\ln\\ln k}{\\ln k}\\right). \\] Thus the class admits an $o(k^3)$ binding function. We also prove the explicit bound \\[ χ(G)\\le \\frac{k^3}{8}+\\frac{5k^2}{4}-4k+8 \\qquad(k\\ge8), \\] with a sharper formula for odd $k$. A further refinement gives an explicit cubic bound with leading coefficient $104/837<1/8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.23441",
  "author_total": 1,
  "authors": [
    {
      "name": "Lizhong Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52df5fzcrz9xe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23441",
  "fulltext_url": null,
  "id": "52df5fzcrz9xe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23441",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7171558595",
  "pdf_url": "https://arxiv.org/pdf/2607.23441",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52df5fzcrz9xe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2607.23441",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23441"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Explicit and logarithmically improved chromatic bounds for $(P_2\\cup P_3)$-free graphs",
  "title_text": "Explicit and logarithmically improved chromatic bounds for (P_2∪ P_3)-free graphs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/52df5fzcrz9xe",
  "venue": "arXiv",
  "versions": []
}