{
  "id": "1212.3940",
  "version": "v1",
  "published": "2012-12-17T09:17:37.000Z",
  "updated": "2012-12-17T09:17:37.000Z",
  "title": "3-Factor-criticality of vertex-transitive graphs",
  "authors": [
    "Heping Zhang",
    "Wuyang Sun"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph of order $n$ is $p$-factor-critical, where $p$ is an integer of the same parity as $n$, if the removal of any set of $p$ vertices results in a graph with a perfect matching. 1-Factor-critical graphs and 2-factor-critical graphs are factor-critical graphs and bicritical graphs, respectively. It is well known that every connected vertex-transitive graph of odd order is factor-critical and every connected non-bipartite vertex-transitive graph of even order is bicritical. In this paper, we show that a simple connected vertex-transitive graph of odd order at least 5 is 3-factor-critical if and only if it is not a cycle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-17T09:17:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "odd order",
      "vertices results",
      "connected non-bipartite vertex-transitive graph",
      "simple connected vertex-transitive graph",
      "factor-critical graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3940Z"
    }
  }
}