{
  "id": "1007.0418",
  "version": "v1",
  "published": "2010-07-02T18:09:17.000Z",
  "updated": "2010-07-02T18:09:17.000Z",
  "title": "Star clusters in independence complexes of graphs",
  "authors": [
    "Jonathan Ariel Barmak"
  ],
  "comment": "22 pages, 13 figures",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "We introduce the notion of \\textit{star cluster} of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen from works of Engstr\\\"om and Jonsson on the homotopy type of independence complexes of triangle-free graphs and to investigate a large number of examples which appear in the literature. We present an alternative way to study the chromatic number of a graph from a homotopical point of view and obtain new results regarding the connectivity of independence complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-02T18:09:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "05C69",
      "55P15",
      "05C10"
    ],
    "keywords": [
      "independence complexes",
      "star clusters",
      "general tool",
      "simplicial complex",
      "homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0418B"
    }
  }
}