{
  "id": "1603.01440",
  "version": "v1",
  "published": "2016-03-04T12:48:04.000Z",
  "updated": "2016-03-04T12:48:04.000Z",
  "title": "Cubic graphs and related triangulations on orientable surfaces",
  "authors": [
    "Wenjie Fang",
    "Mihyun Kang",
    "Michael Moßhammer",
    "Philipp Sprüssel"
  ],
  "comment": "50 pages. An extended abstract of this paper has been published in the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb15), Electronic Notes in Discrete Mathematics (2015), 603--610",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathbb{S}_g$ be the orientable surface of genus $g$. We show that the number of vertex-labelled cubic multigraphs embeddable on $\\mathbb{S}_g$ with $2n$ vertices is asymptotically $c_g n^{5(g-1)/2-1}\\gamma^{2n}(2n)!$, where $\\gamma$ is an algebraic constant and $c_g$ is a constant depending only on the genus $g$. We also derive an analogous result for simple cubic graphs and weighted cubic multigraphs. Additionally we prove that a typical cubic multigraph embeddable on $\\mathbb{S}_g$, $g\\ge 1$, has exactly one non-planar component.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-04T12:48:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05C10",
      "05C30",
      "57M15"
    ],
    "keywords": [
      "orientable surface",
      "related triangulations",
      "simple cubic graphs",
      "vertex-labelled cubic multigraphs",
      "typical cubic multigraph"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301440F"
    }
  }
}