{
  "id": "1602.02291",
  "version": "v1",
  "published": "2016-02-06T18:52:42.000Z",
  "updated": "2016-02-06T18:52:42.000Z",
  "title": "Discrepancy and Eigenvalues of Cayley Graphs",
  "authors": [
    "Yoshiharu Kohayakawa",
    "Vojtěch Rödl",
    "Mathias Schacht"
  ],
  "comment": "Dedicated to the memory of Professor Miroslav Fiedler",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This positively answers a question of Chung and Graham [\"Sparse quasi-random graphs\", Combinatorica 22 (2002), no. 2, 217-244] for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-06T18:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C80"
    ],
    "keywords": [
      "cayley graphs",
      "sparse quasi-random graphs",
      "finite abelian groups",
      "large eigenvalue gap",
      "quasirandom properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202291K"
    }
  }
}