{
  "id": "2009.04305",
  "version": "v1",
  "published": "2020-09-09T13:59:11.000Z",
  "updated": "2020-09-09T13:59:11.000Z",
  "title": "Leighton's Theorem: extensions, limitations, and quasitrees",
  "authors": [
    "Martin R. Bridson",
    "Sam Shepherd"
  ],
  "comment": "29 pages, 9 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Leighton's Theorem states that if there is a tree $T$ that covers two finite graphs $G_1$ and $G_2$, then there is a finite graph $\\hat G$ that is covered by $T$ and covers both $G_1$ and $G_2$. We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to non-regular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-09T13:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "05C25"
    ],
    "keywords": [
      "limitations",
      "finite graph",
      "extensions",
      "leightons theorem states",
      "regular coverings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}