{
  "id": "1509.06393",
  "version": "v1",
  "published": "2015-09-21T20:30:42.000Z",
  "updated": "2015-09-21T20:30:42.000Z",
  "title": "Decomposing highly edge-connected graphs into paths of any given length",
  "authors": [
    "Fabio Botler",
    "Guilherme O. Mota",
    "Marcio T. I. Oshiro",
    "Yoshiko Wakabayashi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In 2006, Bar\\'at and Thomassen posed the following conjecture: for each tree $T$, there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $|E(G)|$ is divisible by $|E(T)|$, then $G$ admits a decomposition into copies of $T$. This conjecture was verified for stars, some bistars, paths of length $3$, $5$, and $2^r$ for every positive integer $r$. We prove that this conjecture holds for paths of any fixed length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-21T20:30:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B40",
      "05C70",
      "05C51",
      "05C38",
      "05C40"
    ],
    "keywords": [
      "decomposing highly edge-connected graphs",
      "conjecture holds",
      "natural number",
      "decomposition",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906393B"
    }
  }
}