{
  "id": "0905.3487",
  "version": "v1",
  "published": "2009-05-21T13:15:37.000Z",
  "updated": "2009-05-21T13:15:37.000Z",
  "title": "A Simple Proof of an Inequality Connecting the Alternating Number of Independent Sets and the Decycling Number",
  "authors": [
    "Vadim E. Levit",
    "Eugen Mandrescu"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "If alpha=alpha(G) is the maximum size of an independent set and s_{k} equals the number of stable sets of cardinality k in graph G, then I(G;x)=s_{0}+s_{1}x+...+s_{alpha}x^{alpha} is the independence polynomial of G. In this paper we provide an elementary proof of the inequality claiming that the absolute value of I(G;-1) is not greater than 2^phi(G), for every graph G, where phi(G) is its decycling number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-21T13:15:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05A20",
      "52B05",
      "57M15"
    ],
    "keywords": [
      "independent set",
      "decycling number",
      "simple proof",
      "alternating number",
      "inequality connecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3487L"
    }
  }
}