{
  "id": "1504.07388",
  "version": "v1",
  "published": "2015-04-28T09:17:14.000Z",
  "updated": "2015-04-28T09:17:14.000Z",
  "title": "Topological minors of cover graphs and dimension",
  "authors": [
    "Piotr Micek",
    "Veit Wiechert"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce new tools to tackle problems involving upper bounds on poset dimension. Using these tools we prove two results: (1) Posets of bounded height whose cover graphs exclude a fixed graph as a topological minor have bounded dimension; (2) The $(k+k)$-free posets whose cover graphs exclude a fixed graph as a topological minor contain only standard examples of size bounded in terms of $k$. The first result was already given by Walczak. Our argument is very different, elementary, and in particular does not rely on structural decomposition theorems. The second result supports a conjectured generalization of the first result for $(k+k)$-free posets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-28T09:17:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cover graphs exclude",
      "free posets",
      "first result",
      "fixed graph",
      "structural decomposition theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407388M"
    }
  }
}