{
  "id": "2406.07718",
  "version": "v1",
  "published": "2024-06-11T20:57:24.000Z",
  "updated": "2024-06-11T20:57:24.000Z",
  "title": "Non-spherical sets versus lines in Euclidean Ramsey theory",
  "authors": [
    "David Conlon",
    "Jakob Führer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for every non-spherical set $X$ in $\\mathbb{E}^d$, there exists a natural number $m$ and a red/blue-colouring of $\\mathbb{E}^n$ for every $n$ such that there is no red copy of X and no blue progression of length $m$ with each consecutive point at distance $1$. This verifies a conjecture of Wu and the first author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-11T20:57:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "52C10"
    ],
    "keywords": [
      "euclidean ramsey theory",
      "non-spherical set",
      "natural number",
      "blue progression",
      "first author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}