{
  "id": "1309.1284",
  "version": "v1",
  "published": "2013-09-05T09:06:33.000Z",
  "updated": "2013-09-05T09:06:33.000Z",
  "title": "On Roussel-Rubio-type lemmas and their consequences",
  "authors": [
    "Nicolas Trotignon",
    "Kristina Vušković"
  ],
  "journal": "Discrete Mathematics, 311(8-9):684-687, 2011",
  "doi": "10.1002/jgt.20405",
  "categories": [
    "math.CO"
  ],
  "abstract": "Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward's decomposition theorem for weakly chordal graphs, relying on a Roussel--Rubio-type lemma. We recall how Roussel--Rubio-type lemmas yield very short proofs of the existence of even pairs in weakly chordal graphs and Meyniel graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-05T09:06:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C17"
    ],
    "keywords": [
      "short proof",
      "weakly chordal graphs",
      "consequences",
      "strong perfect graph theorem",
      "roussel-rubio-type lemmas yield"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1284T"
    }
  }
}