{
  "id": "2007.15127",
  "version": "v1",
  "published": "2020-07-29T21:56:40.000Z",
  "updated": "2020-07-29T21:56:40.000Z",
  "title": "On the connectivity of the disjointness graph of segments of point sets in general position in the plane",
  "authors": [
    "J. Leaños",
    "M. K. Christophe Ndjatchi",
    "L. M. Ríos-Castro"
  ],
  "comment": "12 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $P$ be a set of $n\\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in $D(P)$ if and only if they are disjoint. We show that the connectivity of $D(P)$ is at least $\\binom{\\lfloor\\frac{n-2}{2}\\rfloor}{2}+\\binom{\\lceil\\frac{n-2}{2}\\rceil}{2}$, and that this bound is tight for each $n\\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-29T21:56:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40"
    ],
    "keywords": [
      "general position",
      "point sets",
      "connectivity",
      "closed straight line segments",
      "edge disjointness graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}