{
  "id": "math/0406053",
  "version": "v1",
  "published": "2004-06-03T06:14:29.000Z",
  "updated": "2004-06-03T06:14:29.000Z",
  "title": "A Note on Graph Pebbling",
  "authors": [
    "Andrzej Czygrinow",
    "Glenn Hurlbert",
    "Hal Kierstead",
    "Tom Trotter"
  ],
  "comment": "12 pages",
  "journal": "Graphs and Combinatorics 18 (2002), 219--225",
  "categories": [
    "math.CO"
  ],
  "abstract": "We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d)=\\Omega(2^d/d). In this note, we show that k exists and satisfies k(d)=O(2^{2d}). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-03T06:14:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "graph pebbling",
      "positive integer",
      "random graph threshold",
      "upper bound",
      "connectivity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6053C"
    }
  }
}