{
  "id": "1504.06234",
  "version": "v1",
  "published": "2015-04-23T15:58:52.000Z",
  "updated": "2015-04-23T15:58:52.000Z",
  "title": "Acyclic chromatic index of triangle-free $1$-planar graphs",
  "authors": [
    "Jijuan Chen",
    "Tao Wang",
    "Huiqin Zhang"
  ],
  "comment": "7 pages. arXiv admin note: substantial text overlap with arXiv:1302.2405, arXiv:1405.0713",
  "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 $\\Delta(G)$. A graph is {\\em $1$-planar} if it can be drawn on the plane such that every edge is crossed by at most one other edge. In this paper, we prove that every triangle-free $1$-planar graph $G$ admits an acyclic edge coloring with $\\Delta(G) + 17$ colors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-23T15:58:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "acyclic chromatic index",
      "planar graph",
      "acyclic edge coloring",
      "triangle-free",
      "maximum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406234C"
    }
  }
}