{
  "id": "1412.8358",
  "version": "v1",
  "published": "2014-12-29T14:51:24.000Z",
  "updated": "2014-12-29T14:51:24.000Z",
  "title": "Odd graphs and its application on the strong edge coloring",
  "authors": [
    "Tao Wang",
    "Xiaodan Zhao"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index $\\chiup_{s}'(G)$ of a graph $G$ is the minimum number of colors in a strong edge coloring of $G$. Let $\\Delta \\geq 4$ be an integer. In this note, we study the properties of the odd graphs, and show that every planar graph with maximum degree at most $\\Delta$ and girth at least $10 \\Delta - 4$ has a strong edge coloring using $2\\Delta - 1$ colors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-29T14:51:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "strong edge coloring",
      "odd graphs",
      "application",
      "strong chromatic index",
      "color class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8358W"
    }
  }
}