{
  "id": "1709.06854",
  "version": "v1",
  "published": "2017-09-20T13:40:10.000Z",
  "updated": "2017-09-20T13:40:10.000Z",
  "title": "A note on the 4-girth-thickness of K_{n,n,n}",
  "authors": [
    "Xia Guo",
    "Yan Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The $4$-girth-thickness $\\theta(4,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least four whose union is $G$. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph $K_{n,n,n}$ is $\\big\\lceil\\frac{n+1}{2}\\big\\rceil$ except for $\\theta(4,K_{1,1,1})=2$. And we also show that the $4$-girth-thickness of the complete graph $K_{10}$ is three which disprove the conjecture $\\theta(4,K_{10})=4$ posed by Rubio-Montiel (Ars Math Contemp 14(2) (2018) 319).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-20T13:40:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ars math contemp",
      "complete tripartite graph",
      "minimum number",
      "planar subgraphs",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}