{
  "id": "1005.0582",
  "version": "v1",
  "published": "2010-05-04T16:49:51.000Z",
  "updated": "2010-05-04T16:49:51.000Z",
  "title": "An extremal theorem in the hypercube",
  "authors": [
    "David Conlon"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The hypercube Q_n is the graph whose vertex set is {0,1}^n and where two vertices are adjacent if they differ in exactly one coordinate. For any subgraph H of the cube, let ex(Q_n, H) be the maximum number of edges in a subgraph of Q_n which does not contain a copy of H. We find a wide class of subgraphs H, including all previously known examples, for which ex(Q_n, H) = o(e(Q_n)). In particular, our method gives a unified approach to proving that ex(Q_n, C_{2t}) = o(e(Q_n)) for all t >= 4 other than 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-04T16:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "extremal theorem",
      "vertex set",
      "maximum number",
      "wide class",
      "coordinate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.0582C"
    }
  }
}