{
  "id": "1110.0224",
  "version": "v1",
  "published": "2011-10-02T20:07:52.000Z",
  "updated": "2011-10-02T20:07:52.000Z",
  "title": "On a covering problem in the hypercube",
  "authors": [
    "Brendon Stanton",
    "Lale Özkahya"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we address a particular variation of the Tur\\'an problem for the hypercube. Alon, Krech and Szab\\'o (2007) asked \"In an n-dimensional hypercube, Qn, and for l < d < n, what is the size of a smallest set, S, of Q_l's so that every Q_d contains at least one member of S?\" Likewise, they asked a similar Ramsey type question: \"What is the largest number of colors that we can use to color the copies of Q_l in Q_n such that each Q_d contains a Q_l of each color?\" We give upper and lower bounds for each of these questions and provide constructions of the set S above for some specific cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-02T20:07:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "covering problem",
      "similar ramsey type question",
      "turan problem",
      "specific cases",
      "n-dimensional hypercube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0224S"
    }
  }
}