{
  "id": "2010.13195",
  "version": "v1",
  "published": "2020-10-25T19:10:41.000Z",
  "updated": "2020-10-25T19:10:41.000Z",
  "title": "A family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by nine points",
  "authors": [
    "Daniel McGinnis"
  ],
  "comment": "The author was supported by NSF grant DMS-1839918 (RTG)",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that every finite family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by $9$ points. This improves the bound of $13$ proved by Gy\\'arf\\'as, Kleitman, and T\\'oth in 2001.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-25T19:10:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex sets",
      "plane satisfying"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}