{
  "id": "2306.14249",
  "version": "v1",
  "published": "2023-06-25T13:47:20.000Z",
  "updated": "2023-06-25T13:47:20.000Z",
  "title": "A Dyck-word tree that controls all odd graphs",
  "authors": [
    "Italo J. Dejter"
  ],
  "comment": "23 pages, 12 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "An infinite ordered tree $T$ exists that has as its vertex set a collection of tight restricted-growth strings representing all Dyck words; these stand for the cyclic (resp., dihedral) classes and uniform 2-factor cycles of odd graphs (resp., middle-levels graphs). Odd graphs have edge-supplementary arc-factorizations based on Dyck words which, represented as Dyck nests, possess a signature admitting universal updates along $T$ and allowing an arc-factorization view of the Hamilton cycles found by T. M\\\"utze et al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-25T13:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C38",
      "05C75",
      "68R15"
    ],
    "keywords": [
      "odd graphs",
      "dyck-word tree",
      "dyck words",
      "signature admitting universal updates",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}