{
  "id": "2208.13513",
  "version": "v1",
  "published": "2022-08-29T11:31:11.000Z",
  "updated": "2022-08-29T11:31:11.000Z",
  "title": "More on lines in Euclidean Ramsey theory",
  "authors": [
    "David Conlon",
    "Yu-Han Wu"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\ell_m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\\mathbb{E}^n$ for every $n$ that contains no red copy of $\\ell_3$ and no blue copy of $\\ell_m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-29T11:31:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean ramsey theory",
      "blue copy",
      "natural number",
      "first author",
      "consecutive points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}