{
  "id": "1612.08306",
  "version": "v1",
  "published": "2016-12-25T23:22:14.000Z",
  "updated": "2016-12-25T23:22:14.000Z",
  "title": "On degree-colorings of multigraphs",
  "authors": [
    "Mark K. Goldberg"
  ],
  "comment": "5 pages; 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A notion of degree-coloring is introduced; it captures some, but not all properties of standard edge-coloring. We conjecture that the smallest number of colors needed for degree-coloring of a multigraph $G$ [the degree-coloring index $\\tau(G)$] equals $\\max\\{\\Delta, \\omega\\}$, where $\\Delta$ and $\\omega$ are the maximum vertex degree in $G$ and the multigraph density, respectively. We prove that the conjecture holds iff $\\tau(G)$ is a monotone function on the set of multigraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-25T23:22:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum vertex degree",
      "smallest number",
      "monotone function",
      "multigraph density",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}