{
  "id": "1303.3198",
  "version": "v2",
  "published": "2013-03-13T16:04:43.000Z",
  "updated": "2013-03-30T07:59:00.000Z",
  "title": "1,2,3-Conjecture and 1,2-Conjecture for Sparse Graphs",
  "authors": [
    "Daniel W. Cranston",
    "Sogol Jahanbekam",
    "Douglas B. West"
  ],
  "comment": "29 pages, 19 figures; same results as earlier version, but revised introduction",
  "categories": [
    "math.CO"
  ],
  "abstract": "We apply the Discharging Method to prove the 1,2,3-Conjecture and the 1,2-Conjecture for graphs with maximum average degree less than 8/3. Stronger results on these conjectures have been proved, but this is the first application of discharging to them, and the structure theorems and reducibility results are of independent interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-30T07:59:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sparse graphs",
      "maximum average degree",
      "reducibility results",
      "structure theorems",
      "first application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3198C"
    }
  }
}