{
  "id": "2402.12567",
  "version": "v2",
  "published": "2024-02-19T21:46:58.000Z",
  "updated": "2024-12-16T09:39:28.000Z",
  "title": "Progressions in Euclidean Ramsey theory",
  "authors": [
    "Jakob Führer",
    "Géza Tóth"
  ],
  "journal": "European Journal of Combinatorics, Volume 125, 2025, 104105",
  "doi": "10.1016/j.ejc.2024.104105",
  "categories": [
    "math.CO"
  ],
  "abstract": "Conlon and Wu showed that there is a red/blue-coloring of $\\mathbb{E}^n$ that does not contain $3$ red collinear points separated by unit distance and $m=10^{50}$ blue collinear points separated by unit distance. We prove that the statement holds with $m=1177$. We show similar results with different distances between the points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-16T09:39:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "05D10",
      "11B25",
      "52C99"
    ],
    "keywords": [
      "euclidean ramsey theory",
      "progressions",
      "unit distance",
      "blue collinear points",
      "red collinear points"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}