{
  "id": "0911.4340",
  "version": "v1",
  "published": "2009-11-23T08:52:22.000Z",
  "updated": "2009-11-23T08:52:22.000Z",
  "title": "Regular embeddings of complete bipartite graphs: classification and enumeration",
  "authors": [
    "Gareth A. Jones"
  ],
  "comment": "32 pages",
  "doi": "10.1112/plms/pdp061",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The regular embeddings of complete bipartite graphs $K_{n,n}$ in orientable surfaces are classified and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in the cases where $n$ is a prime power, obtained in collaboration with Du, Kwak, Nedela and \\v{S}koviera, together with results of It\\^o, Hall, Huppert and Wielandt on factorisable groups and on finite solvable groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-23T08:52:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C25",
      "05C30",
      "20D10",
      "20F16"
    ],
    "keywords": [
      "complete bipartite graphs",
      "regular embeddings",
      "enumeration",
      "combinatorial properties",
      "automorphism groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4340J"
    }
  }
}