{
  "id": "1009.3900",
  "version": "v1",
  "published": "2010-09-20T17:50:38.000Z",
  "updated": "2010-09-20T17:50:38.000Z",
  "title": "The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes",
  "authors": [
    "Jonathan Ariel Barmak"
  ],
  "comment": "2 pages",
  "categories": [
    "math.CO",
    "math.AT",
    "math.LO"
  ],
  "abstract": "For each finite simple graph $G$, Aharoni, Berger and Ziv consider a recursively defined number $\\psi (G) \\in \\mathbb{Z}\\cup \\{+ \\infty \\}$ which gives a lower bound for the topological connectivity of the independence complex $I_G$. They conjecture that this bound is optimal for every graph. We use a result of recursion theory to give a short disproof of this claim.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-20T17:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "55P99",
      "03D80",
      "57M05"
    ],
    "keywords": [
      "word problem",
      "aharoni-berger-ziv conjecture",
      "independence complexes",
      "connectivity",
      "finite simple graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3900B"
    }
  }
}