{
  "id": "2405.06446",
  "version": "v1",
  "published": "2024-05-10T12:52:36.000Z",
  "updated": "2024-05-10T12:52:36.000Z",
  "title": "Recoloring via modular decomposition",
  "authors": [
    "Manoj Belavadi",
    "Kathie Cameron",
    "Ni Luh Dewi Sintiari"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The reconfiguration graph of the $k$-colorings of a graph $G$, denoted $R_{k}(G)$, is the graph whose vertices are the $k$-colorings of $G$ and two colorings are adjacent in $R_{k}(G)$ if they differ in color on exactly one vertex. A graph $G$ is said to be recolorable if $R_{\\ell}(G)$ is connected for all $\\ell \\geq \\chi(G)$+1. We use the modular decomposition of several graph classes to prove that the graphs in the class are recolorable. In particular, we prove that every ($P_5$, diamond)-free graph, every ($P_5$, house, bull)-free graph, and every ($P_5$, $C_5$, co-fork)-free graph is recolorable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-10T12:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "modular decomposition",
      "recoloring",
      "reconfiguration graph",
      "graph classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}