{
  "id": "2007.09204",
  "version": "v1",
  "published": "2020-07-17T19:42:15.000Z",
  "updated": "2020-07-17T19:42:15.000Z",
  "title": "Edge-critical subgraphs of Schrijver graphs II: The general case",
  "authors": [
    "Tomáš Kaiser",
    "Matěj Stehlík"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a simple combinatorial description of an $(n-2k+2)$-chromatic edge-critical subgraph of the Schrijver graph $\\mathrm{SG}(n,k)$, itself an induced vertex-critical subgraph of the Kneser graph $\\mathrm{KG}(n,k)$. This extends the main result of [J. Combin. Theory Ser. B 144 (2020) 191--196] to all values of $k$, and sharpens the classical results of Lov\\'asz and Schrijver from the 1970s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-17T19:42:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "schrijver graph",
      "general case",
      "simple combinatorial description",
      "chromatic edge-critical subgraph",
      "kneser graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}