{
  "abstract": "Recently, Heath, McCourt, Parker, Schwieder, and Zerbib initiated the systematic study of the $r$-Kneser Ramsey number $R_r^{KG}(s,t)$ and investigated related Ramsey-type problems. A central motivation for their work comes from a question of Holmsen, Hrusak, and Roldán-Pensado, who asked whether, for $n=2k-1$ and sufficiently large $k$, every red/blue edge-coloring of the complete graph on the vertex set $V = \\binom{[n]}{k}$ necessarily contains a monochromatic triangle $ABC$ with $A,B,C \\in V$ and $A \\cap B \\cap C = \\emptyset$. Heath, McCourt, Parker, Schwieder, and Zerbib established that this conclusion holds when $n \\ge \\frac{7k}{3}$ and $k\\ge 12$. We make substantial progress toward the problem of Holmsen, Hrusak, and Roldán-Pensado by proving that the conclusion already holds for every $k\\ge 2$ whenever $n\\ge 2k+1$. In addition, we obtain improved lower bounds for $R_r^{KG}(s,t)$ when $s$ and $t$ are fixed and $r$ is sufficiently large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27157",
  "author_total": 1,
  "authors": [
    {
      "name": "Igor Araujo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1k4gfq311bpqw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27157",
  "fulltext_url": null,
  "id": "1k4gfq311bpqw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27157",
  "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/2609.27157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1k4gfq311bpqw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27157"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Monochromatic triangles with empty intersection and Kneser Ramsey numbers",
  "title_text": "Monochromatic triangles with empty intersection and Kneser Ramsey numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1k4gfq311bpqw",
  "venue": "arXiv",
  "versions": []
}