{
  "id": "1405.0713",
  "version": "v2",
  "published": "2014-05-04T16:24:55.000Z",
  "updated": "2015-08-26T01:10:22.000Z",
  "title": "Further result on acyclic chromatic index of planar graphs",
  "authors": [
    "Tao Wang",
    "Yaqiong Zhang"
  ],
  "comment": "23 pages, 20 figures, mainly revised Lemma 8 in Discrete Applied Mathematics, 2015. arXiv admin note: text overlap with arXiv:1302.2405",
  "doi": "10.1016/j.dam.2015.07.015",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "An acyclic edge coloring of a graph $G$ is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index $\\chiup_{a}'(G)$ of a graph $G$ is the least number of colors in an acyclic edge coloring of $G$. It was conjectured that $\\chiup'_{a}(G)\\leq \\Delta(G) + 2$ for any simple graph $G$ with maximum degree $\\Delta(G)$. In this paper, we prove that every planar graph $G$ admits an acyclic edge coloring with $\\Delta(G) + 6$ colors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-04T16:24:55.000Z",
      "comment": "23 pages. arXiv admin note: text overlap with arXiv:1302.2405",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-26T01:10:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "acyclic chromatic index",
      "planar graph",
      "acyclic edge coloring",
      "simple graph",
      "maximum degree"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0713W"
    }
  }
}