{
  "id": "1602.07400",
  "version": "v1",
  "published": "2016-02-24T05:07:49.000Z",
  "updated": "2016-02-24T05:07:49.000Z",
  "title": "3-regular colored graphs and classification of surfaces",
  "authors": [
    "Biplab Basak"
  ],
  "comment": "9 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by the theory of crystallizations, we consider an equivalence relation on the class of $3$-regular colored graphs and proved that up to this equivalence $(a)$ there exists a unique contracted 3-regular colored graph if the number of vertices is $4m$ and $(b)$ there are exactly two such graphs if the number of vertices is $4m+2$ for $m\\geq 1$. Using this, we present a simple proof of the classification of closed surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-24T05:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10",
      "57Q15",
      "57N05",
      "57Q05"
    ],
    "keywords": [
      "classification",
      "equivalence relation",
      "regular colored graphs",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}