{
  "id": "2110.08870",
  "version": "v2",
  "published": "2021-10-17T17:11:07.000Z",
  "updated": "2022-06-21T09:50:58.000Z",
  "title": "Gallai's path decomposition in planar graphs",
  "authors": [
    "Alexandre Blanché",
    "Marthe Bonamy",
    "Nicolas Bonichon"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1968, Gallai conjectured that the edges of any connected graph with $n$ vertices can be partitioned into $\\lceil \\frac{n}{2} \\rceil$ paths. We show that this conjecture is true for every planar graph. More precisely, we show that every connected planar graph except $K_3$ and $K_5^-$ ($K_5$ minus one edge) can be decomposed into $\\lfloor \\frac{n}{2} \\rfloor$ paths.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-21T09:50:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gallais path decomposition",
      "connected planar graph",
      "conjecture",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}