{
  "id": "0912.0720",
  "version": "v1",
  "published": "2009-12-03T19:52:37.000Z",
  "updated": "2009-12-03T19:52:37.000Z",
  "title": "Independence Complexes of Stable Kneser Graphs",
  "authors": [
    "Benjamin Braun"
  ],
  "comment": "submitted",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "For integers n\\geq 1, k\\geq 0, the stable Kneser graph SG_{n,k} (also called the Schrijver graph) has as vertex set the stable n-subsets of [2n+k] and as edges disjoint pairs of n-subsets, where a stable n-subset is one that does not contain any 2-subset of the form {i,i+1} or {1,2n+k}. The stable Kneser graphs have been an interesting object of study since the late 1970's when A. Schrijver determined that they are a vertex critical class of graphs with chromatic number k+2. This article contains a study of the independence complexes of SG_{n,k} for small values of n and k. Our contributions are two-fold: first, we find that the homotopy type of the independence complex of SG_{2,k} is a wedge of spheres of dimension two. Second, we determine the homotopy types of the independence complexes of certain graphs related to SG_{n,2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-03T19:52:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "57M15"
    ],
    "keywords": [
      "stable kneser graph",
      "independence complexes",
      "homotopy type",
      "edges disjoint pairs",
      "stable n-subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.0720B"
    }
  }
}