{
  "id": "2010.12668",
  "version": "v1",
  "published": "2020-10-23T21:04:18.000Z",
  "updated": "2020-10-23T21:04:18.000Z",
  "title": "What percent of the plane can be properly 5- and 6-colored?",
  "authors": [
    "Jaan Parts"
  ],
  "journal": "Geombinatorics 30/1 (2020) 25-39",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors. It is thus shown that any unit-distance graph of order at most 6992 and 24 in the plane can be properly 6-colored and 5-colored, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-23T21:04:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean plane",
      "unit-distance graph",
      "uncovered fraction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}