{
  "id": "math/0703544",
  "version": "v1",
  "published": "2007-03-19T10:10:32.000Z",
  "updated": "2007-03-19T10:10:32.000Z",
  "title": "The decycling numbers of graphs",
  "authors": [
    "S. Bau",
    "L. W. Beineke"
  ],
  "journal": "Australasian Journal of Combinatorics 25(2002), 285-298",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G$ and $S\\subset V(G)$, if $G - S$ is acyclic, then $S$ is said to be a decycling set of $G$. The size of a smallest decycling set of $G$ is called the decycling number of $G$. The purpose of this paper is a comprehensive review of recent results and several open problems on this graph parameter. Results to be reviewed include recent work on decycling numbers of cubes, grids and snakes. A structural description of graphs with a fixed decycling number based on connectivity is also presented. Graphs with small decycling numbers are characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-19T10:10:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C45"
    ],
    "keywords": [
      "graph parameter",
      "smallest decycling set",
      "structural description",
      "small decycling numbers",
      "open problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3544B"
    }
  }
}