{
  "id": "1205.1170",
  "version": "v1",
  "published": "2012-05-06T01:32:07.000Z",
  "updated": "2012-05-06T01:32:07.000Z",
  "title": "A De Bruijn-Erdos theorem for 1-2 metric spaces",
  "authors": [
    "Vasek Chvatal"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A special case of a combinatorial theorem of De Bruijn and Erdos asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals 1 or 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-06T01:32:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99",
      "51G99"
    ],
    "keywords": [
      "metric spaces",
      "bruijn-erdos theorem",
      "nonzero distance equals",
      "erdos asserts",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1170C"
    }
  }
}