{
  "id": "2110.08938",
  "version": "v2",
  "published": "2021-10-17T22:24:18.000Z",
  "updated": "2022-09-21T23:59:55.000Z",
  "title": "2-limited broadcast domination in grid graphs",
  "authors": [
    "Aaron Slobodin",
    "Gary MacGillivray",
    "Wendy Myrvold"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit constructions. The lower bounds are obtained via linear programming duality by finding lower bounds for the fractional 2-limited multipacking numbers of these graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-21T23:59:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grid graphs",
      "broadcast domination number",
      "cartesian product",
      "linear programming duality",
      "finding lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}