{
  "id": "1804.09332",
  "version": "v1",
  "published": "2018-04-25T03:15:44.000Z",
  "updated": "2018-04-25T03:15:44.000Z",
  "title": "Spanning trees with at most 4 leaves in $K_{1,5}-$free graphs",
  "authors": [
    "Pham Hoang Ha",
    "Dang Dinh Hanh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ is said to be $K_{1,5}$-free graph if it contains no $K_{1,5}$ as an induced subgraph. Let $\\sigma_5(G)$ denote the minimum degree sum of five independent vertices of a graph $G.$ In this article, we will prove that the connected $K_{1,5}$-free graph $G$ has a spanning tree with at most 4 leaves if $\\sigma_5(G)\\geq |G|-1.$ We also show that the bound $|G|-1$ is sharp. Beside that, a related result also is introduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T03:15:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graph",
      "spanning tree",
      "minimum degree sum",
      "independent vertices",
      "induced subgraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}