{
  "id": "1710.03386",
  "version": "v1",
  "published": "2017-10-10T03:21:22.000Z",
  "updated": "2017-10-10T03:21:22.000Z",
  "title": "Critical ideals, minimum rank and zero forcing number",
  "authors": [
    "Carlos A. Alfaro",
    "Jephian C. -H. Lin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical ideal is trivial. This gives a new perspective for bounding and computing these three graph parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T03:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C50",
      "05E99",
      "13P15",
      "15A03",
      "68W30"
    ],
    "keywords": [
      "zero forcing number",
      "minimum rank",
      "graph parameters",
      "profound relations",
      "th critical ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}