{
  "id": "1809.10761",
  "version": "v1",
  "published": "2018-09-27T20:52:51.000Z",
  "updated": "2018-09-27T20:52:51.000Z",
  "title": "The 1-2-3 Conjecture almost holds for regular graphs",
  "authors": [
    "Jakub Przybyło"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general, while it is known to be possible from the weight set $\\{1,2,3,4,5\\}$. We prove that for regular graphs it is sufficient to use weights $1$, $2$, $3$, $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-27T20:52:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular graphs",
      "vertices receive distinct weighted degrees",
      "adjacent vertices receive distinct",
      "weight set",
      "conjecture asserts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}