{
  "id": "2011.12218",
  "version": "v1",
  "published": "2020-11-24T17:10:25.000Z",
  "updated": "2020-11-24T17:10:25.000Z",
  "title": "Tverberg's theorem, disks, and Hamiltonian cycles",
  "authors": [
    "Pablo Soberón",
    "Yaqian Tang"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a finite set of $S$ points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and for an even set $S$ there exists a Hamiltonian path with the same property. We discuss high-dimensional versions of these theorems and their relation to other results in discrete geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T17:10:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian cycle",
      "tverbergs theorem",
      "discrete geometry",
      "high-dimensional versions",
      "hamiltonian path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}