{
  "id": "2405.09249",
  "version": "v1",
  "published": "2024-05-15T11:04:33.000Z",
  "updated": "2024-05-15T11:04:33.000Z",
  "title": "The DP-coloring of the square of subcubic graphs",
  "authors": [
    "Ren Zhao"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The 2-distance coloring of a graph $G$ is equivalent to the proper coloring of its square graph $G^2$, it is a special distance labeling problem. DP-coloring (or \"Correspondence coloring\") was introduced by Dvo\\v{r}\\'ak and Postle in 2018, to answer a conjecture of list coloring proposed by Borodin. In recent years, many researches pay attention to the DP-coloring of planar graphs with some restriction in cycles. We study the DP-coloring of the square of subcubic graphs in terms of maximum average degree $\\rm{mad}(G)$, and by the discharging method, we showed that: for a subcubic graph $G$, if $\\rm{mad}(G)<9/4$, then $G^2$ is DP-5-colorable; if $\\rm{mad}(G)<12/5$, then $G^2$ is DP-6-colorable. And the bound in the first result is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-15T11:04:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "subcubic graph",
      "dp-coloring",
      "maximum average degree",
      "researches pay attention",
      "special distance labeling problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}