{
  "id": "1907.00380",
  "version": "v1",
  "published": "2019-06-30T13:34:34.000Z",
  "updated": "2019-06-30T13:34:34.000Z",
  "title": "Dimension is polynomial in height for posets with planar cover graphs",
  "authors": [
    "Jakub Kozik",
    "Piotr Micek",
    "William T. Trotter"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We show that height~$h$ posets that have planar cover graphs have dimension $O(h^6)$. Previously, this upper bound was $2^{O(h^3)}$. Planarity plays a key role in our arguments, since there are posets such that (1) dimension is exponential in height and (2) the cover graph excludes $K_5$ as a minor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-30T13:34:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar cover graphs",
      "polynomial",
      "cover graph excludes",
      "planarity plays",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}