{
  "abstract": "For integers $n\\ge m\\ge1$, let $S(n,m)$ be the double star obtained by joining the centers of $K_{1,n}$ and $K_{1,m}$. Ruotolo and Song proved the upper bound $r(S(n,m);k)\\le kn+m+2$ under the condition $(n+1)\\lceil\\frac{n+1}{k-1}\\rceil >m((k-1)n+m)$, as well as the matching lower bound for odd $k$. Zhao, Mao and Zhou proved the matching lower bound for even $k$ and even $n$. We establish the remaining lower bound for even $k\\ge6$ and odd $n$ through a new edge-coloring construction. Combining these results, we obtain $r(S(n,m);k)=kn+m+2$ for all integers $k\\ge5$ and $n\\ge m\\ge1$ satisfying $(n+1)\\lceil\\frac{n+1}{k-1}\\rceil >m((k-1)n+m)$. We also determine the four-color Ramsey number for $m\\ge2$ and odd $n\\ge15m$, showing that $r(S(n,m);4)=4n+m+1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24523",
  "author_total": 1,
  "authors": [
    {
      "name": "Lin Niu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23y7ygs7z27e9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24523",
  "fulltext_url": null,
  "id": "23y7ygs7z27e9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24523",
  "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": "W7223042614",
  "pdf_url": "https://arxiv.org/pdf/2610.24523",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23y7ygs7z27e9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24523",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24523"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Multicolor Ramsey numbers of unbalanced double stars",
  "title_text": "Multicolor Ramsey numbers of unbalanced double stars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/23y7ygs7z27e9",
  "venue": "arXiv",
  "versions": []
}