{
  "id": "1512.05261",
  "version": "v1",
  "published": "2015-12-16T17:48:29.000Z",
  "updated": "2015-12-16T17:48:29.000Z",
  "title": "Ramsey numbers for partially-ordered sets",
  "authors": [
    "Christopher Cox",
    "Derrick Stolee"
  ],
  "comment": "18 pages, 3 figures, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We explore connections to well studied Tur\\'an-type problems in partially-ordered sets, particularly those in the Boolean lattice. We find a strong difference between Ramsey numbers on the Boolean lattice and ordered Ramsey numbers when the partial ordering on the graphs have large antichains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-16T17:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "06A07"
    ],
    "keywords": [
      "partially-ordered sets",
      "ordered ramsey numbers",
      "boolean lattice",
      "form host graphs",
      "arbitrary families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151205261C"
    }
  }
}