{
  "id": "1810.08336",
  "version": "v1",
  "published": "2018-10-19T02:35:19.000Z",
  "updated": "2018-10-19T02:35:19.000Z",
  "title": "A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leaves",
  "authors": [
    "Pham Hoang Ha",
    "Dang Dinh Hanh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $T$ be a tree, a vertex of degree one is called a leaf. The set of leaves of $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$ and denoted by $Stem(T).$ In this note, we give a sharp sufficient condition to show that a $K_{1,t}-$free graph has a spanning tree whose stem has a few leaves. By applying the main result, we give improvements of previous related results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T02:35:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C07",
      "05C69"
    ],
    "keywords": [
      "free graph",
      "spanning tree",
      "sharp sufficient condition",
      "main result",
      "improvements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}