{
  "abstract": "The induced Ramsey number $r_{\\mathrm{ind}}(G,H)$ is defined as the minimum order of a graph $F$ such that any 2-coloring of its edges with red and blue leads to either a red induced copy of $G$ or a blue induced copy of $H$. In 1998, Kohayakawa, Prömel, and Rödl conjectured that for any fixed graph $G$, there exists a constant $f=f(G)$ such that the induced Ramsey number $r_{\\mathrm{ind}}(G, H)$ is bounded by $|V(H)|^f$ for every graph $H$. In this paper, we completely solve the Kohayakawa--Prömel--Rödl conjecture, which states that for any graphs $G$ and $H$ with $|V(G)|=k\\ge2$ and $|V(H)|=t\\ge2$, $r_{\\mathrm{ind}}(G,H)\\le t^{60k^2+3}$. This verifies the conjecture with $f(G)=60|V(G)|^2+3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27478",
  "author_total": 3,
  "authors": [
    {
      "name": "Chuang Zhong"
    },
    {
      "name": "Masaki Kashima"
    },
    {
      "name": "Yaping Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csc2ydcvd5c5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27478",
  "fulltext_url": null,
  "id": "csc2ydcvd5c5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27478",
  "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": "W7223105125",
  "pdf_url": "https://arxiv.org/pdf/2610.27478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csc2ydcvd5c5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Solution to the Kohayakawa-Prömel-Rödl Conjecture",
  "title_text": "A Solution to the Kohayakawa-Prömel-Rödl Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/csc2ydcvd5c5s",
  "venue": "arXiv",
  "versions": []
}