{
  "id": "2105.00206",
  "version": "v1",
  "published": "2021-05-01T10:02:24.000Z",
  "updated": "2021-05-01T10:02:24.000Z",
  "title": "On the Boolean dimension of a graph and other related parameters",
  "authors": [
    "Maurice Pouzet",
    "Hamza Si Kaddour",
    "Bhalchandra D. Thatte"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions and the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the Boolean dimension with the inversion index of a tournament.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-01T10:02:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06F15"
    ],
    "keywords": [
      "boolean dimension",
      "related parameters",
      "symplectic dimensions",
      "inversion index",
      "exact formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}