{
  "id": "2101.03802",
  "version": "v1",
  "published": "2021-01-11T10:30:08.000Z",
  "updated": "2021-01-11T10:30:08.000Z",
  "title": "Circumference of essentially 4-connected planar triangulations",
  "authors": [
    "Igor Fabrici",
    "Jochen Harant",
    "Samuel Mohr",
    "Jens M. Schmidt"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A $3$-connected graph $G$ is essentially $4$-connected if, for any $3$-cut $S\\subseteq V(G)$ of $G$, at most one component of $G-S$ contains at least two vertices. We prove that every essentially $4$-connected maximal planar graph $G$ on $n$ vertices contains a cycle of length at least $\\frac{2}{3}(n+4)$; moreover, this bound is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-11T10:30:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C10"
    ],
    "keywords": [
      "planar triangulations",
      "circumference",
      "connected maximal planar graph",
      "vertices contains",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}