{
  "id": "2207.13244",
  "version": "v1",
  "published": "2022-07-27T02:11:27.000Z",
  "updated": "2022-07-27T02:11:27.000Z",
  "title": "Kempe equivalence of almost bipartite graphs",
  "authors": [
    "Akihiro Higashitani",
    "Naoki Matsumoto"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Two vertex colorings of a graph are Kempe equivalent if they can be transformed into each other by a sequence of switchings of two colors of vertices. It is PSPACE-complete to determine whether two given vertex $k$-colorings of a graph are Kempe equivalent for any fixed $k\\geq 3$, and it is easy to see that every two vertex colorings of any bipartite graph are Kempe equivalent. In this paper, we consider Kempe equivalence of {\\it almost} bipartite graphs which can be obtained from a bipartite graph by adding several edges to connect two vertices in the same partite set. We give a conjecture of Kempe equivalence of such graphs, and we prove several partial solutions and best possibility of the conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-27T02:11:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35",
      "G.2.2"
    ],
    "keywords": [
      "bipartite graph",
      "kempe equivalence",
      "kempe equivalent",
      "vertex colorings",
      "partite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}