{
  "id": "2012.05145",
  "version": "v1",
  "published": "2020-12-09T16:31:31.000Z",
  "updated": "2020-12-09T16:31:31.000Z",
  "title": "Decomposition of $(2k+1)$-regular graphs containing special spanning $2k$-regular Cayley graphs into paths of length $2k+1$",
  "authors": [
    "Fábio Botler",
    "Luiz Hoffmann"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A $P_\\ell$-decomposition of a graph $G$ is a set of paths with $\\ell$ edges in $G$ that cover the edge set of $G$. Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1)$-regular graph that contains a perfect matching admits a $P_{2k+1}$-decomposition. They also verified this conjecture for $5$-regular graphs without cycles of length $4$. In 2015, Botler, Mota, and Wakabayashi verified this conjecture for $5$-regular graphs without triangles. In this paper, we verify it for $(2k+1)$-regular graphs that contain the $k$th power of a spanning cycle; and for $5$-regular graphs that contain special spanning $4$-regular Cayley graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-09T16:31:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C51",
      "05C70",
      "05C38"
    ],
    "keywords": [
      "regular graphs containing special spanning",
      "regular cayley graphs",
      "decomposition",
      "edge set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}