{
  "id": "1808.01548",
  "version": "v1",
  "published": "2018-08-05T01:34:52.000Z",
  "updated": "2018-08-05T01:34:52.000Z",
  "title": "On the number of edges in some graphs",
  "authors": [
    "Chunhui Lai"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that $\\lim\\inf_{n \\to \\infty} {f(n)-n \\over \\sqrt n} \\geq \\sqrt {2 + \\frac{40}{99}},$ which is better than the previous bounds $\\sqrt 2$ [Y. Shi, Discrete Math. 71(1988), 57-71], $\\sqrt {2 + \\frac{7654}{19071}}$ [C. Lai, Discrete Appl. Math. 232 (2017), 226-229]. We show that $\\liminf_{n \\rightarrow \\infty} {g(n,m)-n\\over \\sqrt \\frac{n}{m}} > \\sqrt {2.444},$ for all even integer $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-05T01:34:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C35"
    ],
    "keywords": [
      "discrete appl",
      "discrete math"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}