{
  "id": "1607.01456",
  "version": "v1",
  "published": "2016-07-06T01:57:08.000Z",
  "updated": "2016-07-06T01:57:08.000Z",
  "title": "Decomposing 8-regular graphs into paths of length 4",
  "authors": [
    "Fábio Botler",
    "Alexandre Talon"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A $T$-decomposition of a graph $G$ is a set of edge-disjoint copies of $T$ in $G$ that cover the edge set of $G$. Graham and H\\\"aggkvist (1989) conjectured that any $2\\ell$-regular graph $G$ admits a $T$-decomposition if $T$ is a tree with $\\ell$ edges. Kouider and Lonc (1999) conjectured that, in the special case where $T$ is the path with $\\ell$ edges, $G$ admits a $T$-decomposition $\\mathcal{D}$ where every vertex of $G$ is the end-vertex of exactly two paths of $\\mathcal{D}$, and proved that this statement holds when $G$ has girth at least $(\\ell+3)/2$. In this paper we verify Kouider and Lonc's Conjecture for paths of length $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-06T01:57:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B40",
      "05C70",
      "05C51",
      "05C38"
    ],
    "keywords": [
      "decomposition",
      "edge-disjoint copies",
      "statement holds",
      "decomposing",
      "edge set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}