{
  "id": "1308.4877",
  "version": "v3",
  "published": "2013-08-22T14:31:32.000Z",
  "updated": "2015-01-29T15:54:58.000Z",
  "title": "Posets with cover graph of pathwidth two have bounded dimension",
  "authors": [
    "Csaba Biró",
    "Mitchel T. Keller",
    "Stephen J. Young"
  ],
  "comment": "18 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant $d$ such that if $P$ is a poset with cover graph of $P$ of pathwidth at most $2$, then $\\dim(P)\\leq d$. We answer this question in the affirmative by showing that $d=17$ is sufficient. We also show that if $P$ is a poset containing the standard example $S_5$ as a subposet, then the cover graph of $P$ has treewidth at least $3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-14T15:30:58.000Z",
      "comment": "16 pages, 9 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-29T15:54:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "05C75",
      "05C83"
    ],
    "keywords": [
      "cover graph",
      "bounded dimension",
      "standard example",
      "sufficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4877B"
    }
  }
}