{
  "id": "2212.13096",
  "version": "v1",
  "published": "2022-12-26T11:46:09.000Z",
  "updated": "2022-12-26T11:46:09.000Z",
  "title": "A simple proof for the lower bound of the girth of graphs $D(n, q)$",
  "authors": [
    "Vladislav Taranchuk"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The components of the graphs $D(n, q)$ provide the best-known general lower bound for the number of edges in a graph with $n$ vertices and no cycles of length less than $g$. In this paper, we give a new, short, and simpler proof of the fact that the length of the shortest cycle appearing in $D(n, q)$ is $n + 5$ when $n$ is odd, and $n + 4$ when $n$ is even.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-26T11:46:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple proof",
      "best-known general lower bound",
      "simpler proof",
      "shortest cycle",
      "components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}