{
  "abstract": "For a graph $G$ with $3\\mid e(G)$, let $R(G,\\mathbb Z_3)$ denote the least integer $N$ such that every edge weighting $w:E(K_N)\\to\\mathbb Z_3$ admits a copy of $G$ whose edge weights sum to zero. We prove that every $n$-vertex graph $G$ with $n\\ge6$ and $3\\mid e(G)$ satisfies $R(G,\\mathbb Z_3)\\le n+5$. Moreover, the stronger bound $R(G,\\mathbb Z_3)\\le n+4$ holds whenever $G$ contains an induced $P_4$ or an induced $2K_2$. Consequently, we resolve a problem posed by Caro and Mifsud: every graph $G$ with $3\\mid e(G)$ satisfies $R(G,\\mathbb Z_3)\\le |V(G)|+8$, with equality if and only if $G\\cong K_3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27788",
  "author_total": 2,
  "authors": [
    {
      "name": "Cheng Chi"
    },
    {
      "name": "Jialin He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kdrnjv588jjs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27788",
  "fulltext_url": null,
  "id": "2kdrnjv588jjs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27788",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214150664",
  "pdf_url": "https://arxiv.org/pdf/2609.27788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kdrnjv588jjs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On a problem concerning $\\mathbb Z_3$-Ramsey numbers",
  "title_text": "On a problem concerning ℤ_3-Ramsey numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2kdrnjv588jjs",
  "venue": "arXiv",
  "versions": []
}