{
  "id": "1809.10263",
  "version": "v1",
  "published": "2018-09-26T23:16:38.000Z",
  "updated": "2018-09-26T23:16:38.000Z",
  "title": "Counting Shellings of Complete Bipartite Graphs and Trees",
  "authors": [
    "Yibo Gao",
    "Junyao Peng"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite graphs and trees. For complete bipartite graphs, we obtain an exact formula for their shelling numbers. And for trees, we propose a simple method to count shellings and bound shelling numbers using vertex degrees and diameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T23:16:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete bipartite graphs",
      "counting shellings",
      "abstract simplicial complex",
      "exact formula",
      "vertex degrees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}