{
  "id": "1310.1430",
  "version": "v2",
  "published": "2013-10-05T02:37:23.000Z",
  "updated": "2014-02-25T15:24:08.000Z",
  "title": "An asymptotically tight bound on the Q-index of graphs with forbidden cycles",
  "authors": [
    "V. Nikiforov"
  ],
  "comment": "10 pages. Version 2 takes care of some mistakes in version 1",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be a graph of order n and let q(G) be that largest eigenvalue of the signless Laplacian of G. In this note it is shown that if k>1 and q(G)>=n+2k-2, then G contains cycles of length l whenever 2<l<2k+3. This bound is asymptotically tight. It implies an asymptotic solution to a recent conjecture about the maximum q(G) of a graph G with no cycle of a specified length.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-25T15:24:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "05C50"
    ],
    "keywords": [
      "asymptotically tight bound",
      "forbidden cycles",
      "largest eigenvalue",
      "contains cycles",
      "asymptotic solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.1430N"
    }
  }
}