{
  "id": "1704.05089",
  "version": "v1",
  "published": "2017-04-17T18:46:51.000Z",
  "updated": "2017-04-17T18:46:51.000Z",
  "title": "On the number of points in general position in the plane",
  "authors": [
    "Jozsef Balogh",
    "Jozsef Solymosi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study some Erdos type problems in discrete geometry. Our main result is that we show that there is a planar point set of n points such that no four are collinear but no matter how we choose a subset of size $n^{5/6+o(1)} $ it contains a collinear triple. Another application studies epsilon-nets in a point-line system in the plane. We prove the existence of some geometric constructions with a new tool, the so-called Hypergraph Container Method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-17T18:46:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general position",
      "hypergraph container method",
      "erdos type problems",
      "application studies epsilon-nets",
      "planar point set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}