{
  "id": "1612.07540",
  "version": "v1",
  "published": "2016-12-22T10:53:32.000Z",
  "updated": "2016-12-22T10:53:32.000Z",
  "title": "Planar posets have dimension at most linear in their height",
  "authors": [
    "Gwenaël Joret",
    "Piotr Micek",
    "Veit Wiechert"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove that every planar poset $P$ of height $h$ has dimension at most $192h + 96$. This improves on previous exponential bounds and is best possible up to a constant factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-22T10:53:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar poset",
      "exponential bounds",
      "constant factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}