{
  "id": "1906.06323",
  "version": "v1",
  "published": "2019-06-14T17:57:21.000Z",
  "updated": "2019-06-14T17:57:21.000Z",
  "title": "PSD-throttling on Trees",
  "authors": [
    "Michael S. Ross"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "PSD-forcing is a coloring process on a graph that colors vertices blue by starting with an initial set $B$ of blue vertices and applying a color change rule (CCR-$\\Zp$). The PSD-throttling number is the minimum of the sum of the cardinality of $B$ and the number of the time-steps needed to color the graph (the PSD-propagation time of $B$). Concentration, which is a technique for computing the PSD-throttling number by reducing a tree to a smaller vertex-weighted tree, is introduced and used to determine the PSD-throttling numbers of balanced spiders. It is shown that the PSD-throttling number of a balanced spider does not exceed that of the path of the same order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T17:57:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C57",
      "05C15",
      "05C50"
    ],
    "keywords": [
      "psd-throttling number",
      "colors vertices blue",
      "color change rule",
      "balanced spider",
      "blue vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}