{
  "id": "1708.08865",
  "version": "v1",
  "published": "2017-08-29T16:32:20.000Z",
  "updated": "2017-08-29T16:32:20.000Z",
  "title": "Circumference of 3-connected cubic graphs",
  "authors": [
    "Qinghai Liu",
    "Xingxing Yu",
    "Zhao Zhang"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The circumference of a graph is the length of its longest cycles. Jackson established a conjecture of Bondy by showing that the circumference of a 3-connected cubic graph of order $n$ is $\\Omega(n^{0.694})$. Bilinski {\\it et al.} improved this lower bound to $\\Omega(n^{0.753})$ by studying large Eulerian subgraphs in 3-edge-connected graphs. In this paper, we further improve this lower bound to $\\Omega(n^{0.8})$. This is done by considering certain 2-connected cubic graphs, finding cycles through two given edges, and distinguishing the cases whether or not these edges are adjacent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-29T16:32:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic graph",
      "circumference",
      "lower bound",
      "studying large eulerian subgraphs",
      "longest cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}