{
  "id": "1805.02715",
  "version": "v1",
  "published": "2018-05-07T19:42:57.000Z",
  "updated": "2018-05-07T19:42:57.000Z",
  "title": "Anti-van der Waerden Numbers of Graph Products",
  "authors": [
    "Hunter Rehm",
    "Alex Schulte",
    "Nathan Warnberg"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, anti-van der Waerden numbers on Cartesian products of graphs are investigated and a conjecture made by Schulte, et al (see arXiv:1802.01509) is answered. In particular, the anti-van der Waerden number of the Cartesian product of two graphs has an upper bound of four. This result is then used to determine the anti-van der Waerden number for any Cartesian product of two paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-07T19:42:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anti-van der waerden number",
      "graph products",
      "cartesian product",
      "upper bound",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}