{
  "id": "math/0106066",
  "version": "v1",
  "published": "2001-06-10T07:36:20.000Z",
  "updated": "2001-06-10T07:36:20.000Z",
  "title": "THe largest eigenvalue of sparse random graphs",
  "authors": [
    "Michael Krivelevich",
    "Benny Sudakov"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n,p) satisfies almost surely: \\lambda_1(G)=(1+o(1))max{\\sqrt{\\Delta},np}, where \\Delta is a maximal degree of G, and the o(1) term tends to zero as max{\\sqrt{\\Delta},np} tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-10T07:36:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "15A52"
    ],
    "keywords": [
      "sparse random graphs",
      "largest eigenvalue",
      "maximal degree",
      "edge probability",
      "term tends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6066K"
    }
  }
}