{
  "id": "1209.2471",
  "version": "v1",
  "published": "2012-09-12T00:53:03.000Z",
  "updated": "2012-09-12T00:53:03.000Z",
  "title": "Every 4-regular graph is acyclically edge-6-colorable",
  "authors": [
    "Wang Weifan",
    "Shu Qiaojun",
    "Wang Yiqiao"
  ],
  "comment": "24 pages, 9 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "An acyclic edge coloring of a graph $G$ is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index $a'(G)$ of $G$ is the smallest integer $k$ such that $G$ has an acyclic edge coloring using $k$ colors. Fiam${\\rm \\check{c}}$ik (1978) and later Alon, Sudakov and Zaks (2001) conjectured that $a'(G)\\le \\Delta + 2$ for any simple graph $G$ with maximum degree $\\Delta$. Basavaraju and Chandran (2009) showed that every graph $G$ with $\\Delta=4$, which is not 4-regular, satisfies the conjecture. In this paper, we settle the 4-regular case, i.e., we show that every 4-regular graph $G$ has $a'(G)\\le 6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-12T00:53:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "acyclic edge coloring",
      "acyclic chromatic index",
      "conjecture",
      "maximum degree",
      "proper edge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2471W"
    }
  }
}