{
  "id": "1901.00043",
  "version": "v1",
  "published": "2018-12-31T20:51:27.000Z",
  "updated": "2018-12-31T20:51:27.000Z",
  "title": "On the structure of (claw,bull)-free graphs",
  "authors": [
    "Sebastián González Hermosillo de la Maza",
    "Yifan Jing",
    "Masood Masjoody"
  ],
  "comment": "keywords: graph classes, (claw, bull)-free, triangle-free",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this research, we determine the structure of (claw, bull)-free graphs. We show that every connected (claw, bull)-free graph is either an expansion of a path, an expansion of a cycle, or the complement of a triangle-free graph; where an expansion of a graph $G$ is obtained by replacing its vertices with disjoint cliques and adding all edges between cliques corresponding to adjacent vertices of $G$. This result also reveals facts about the structure of triangle-free graphs, which might be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-31T20:51:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75"
    ],
    "keywords": [
      "triangle-free graph",
      "independent interest",
      "disjoint cliques",
      "adjacent vertices",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}