{
  "id": "1602.02406",
  "version": "v1",
  "published": "2016-02-07T18:46:29.000Z",
  "updated": "2016-02-07T18:46:29.000Z",
  "title": "A decomposition theorem for {ISK4,wheel}-free trigraphs",
  "authors": [
    "Martin Milanič",
    "Irena Penev",
    "Nicolas Trotignon"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of K4 (the complete graph on four vertices). A wheel is a graph that consists of a chordless cycle, together with a vertex that has at least three neighbors in the cycle. A graph is {ISK4,wheel}-free if it has no ISK4 and does not contain a wheel as an induced subgraph. A \"trigraph\" is a generalization of a graph in which some pairs of vertices have \"undetermined\" adjacency. We prove a decomposition theorem for {ISK4,wheel}-free trigraphs. Our proof closely follows the proof of a decomposition theorem for ISK4-free graphs due to L\\'ev\\^eque, Maffray, and Trotignon (On graphs with no induced subdivision of K4. J. Combin. Theory Ser. B, 102(4):924-947, 2012).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-07T18:46:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decomposition theorem",
      "induced subgraph",
      "subdivision",
      "complete graph",
      "isk4-free graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202406M"
    }
  }
}