{
  "id": "1812.09305",
  "version": "v1",
  "published": "2018-12-21T18:38:44.000Z",
  "updated": "2018-12-21T18:38:44.000Z",
  "title": "Isolation of cycles",
  "authors": [
    "Peter Borg"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any graph $G$, let $\\iota_{\\rm c}(G)$ denote the size of a smallest set $D$ of vertices of $G$ such that the graph obtained from $G$ by deleting the closed neighbourhood of $D$ contains no cycle. We prove that if $G$ is a connected $n$-vertex graph that is not a triangle, then $\\iota_{\\rm c}(G) \\leq n/4$. We also show that the bound is sharp. Consequently, we solve a problem of Caro and Hansberg.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-21T18:38:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C69",
      "05C38"
    ],
    "keywords": [
      "smallest set",
      "vertex graph",
      "closed neighbourhood"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}