{
  "id": "1612.07888",
  "version": "v1",
  "published": "2016-12-23T07:14:34.000Z",
  "updated": "2016-12-23T07:14:34.000Z",
  "title": "On the genus of the complete tripartite graph $K_{n,n,1}$",
  "authors": [
    "Valentas Kurauskas"
  ],
  "comment": "15 pages, 6 figures",
  "journal": "Discrete Math, 340 (2017), 508-515",
  "doi": "10.1016/j.disc.2016.09.017",
  "categories": [
    "math.CO"
  ],
  "abstract": "For even $n$ we prove that the genus of the complete tripartite graph $K_{n,n,1}$ is $\\lceil (n-1) (n-2)/4 \\rceil$. This is the least number of bridges needed to build a complete $n$-way road interchange where changing lanes is not allowed. Both the theoretical result, and the surprising link to modelling road intersections are new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-23T07:14:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete tripartite graph",
      "way road interchange",
      "modelling road intersections",
      "changing lanes",
      "theoretical result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}