{
  "id": "1902.05701",
  "version": "v1",
  "published": "2019-02-15T06:17:33.000Z",
  "updated": "2019-02-15T06:17:33.000Z",
  "title": "On a conjecture of Bondy and Vince",
  "authors": [
    "Jun Gao",
    "Jie Ma"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Twenty years ago Bondy and Vince conjectured that for any nonnegative integer $k$, except finitely many counterexamples, every graph with $k$ vertices of degree less than three contains two cycles whose lengths differ by one or two. The case $k\\leq 2$ was proved by Bondy and Vince, which resolved an earlier conjecture of Erd\\H{o}s et. al.. In this paper we confirm this conjecture for all $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-15T06:17:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lengths differ",
      "earlier conjecture",
      "counterexamples",
      "nonnegative integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}