{
  "id": "2005.03218",
  "version": "v1",
  "published": "2020-05-07T03:02:38.000Z",
  "updated": "2020-05-07T03:02:38.000Z",
  "title": "Packing of spanning mixed arborescences",
  "authors": [
    "Hui Gao",
    "Daqing Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we characterize a mixed graph $F$ which contains $k$ edge and arc disjoint spanning mixed arborescences $F_{1}, \\ldots, F_{k}$, such that for each $v \\in V(F)$, the cardinality of $\\{i \\in [k]: v \\text{ is the root of } F_{i}\\}$ lies in some prescribed interval. This generalizes both Nash-Williams and Tutte's theorem on spanning tree packing for undirected graphs and the previous characterization on digraphs which was given by Cai [in: Arc-disjoint arborescences of digraphs, J. Graph Theory 7(2) (1983), 235-240] and Frank [in: On disjoint trees and arborescences, Algebraic Methods in Graph Theory, Colloquia Mathematica Soc. J. Bolyai, Vol. 25 (North-Holland, Amsterdam) (1978), 159-169].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-07T03:02:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graph theory",
      "colloquia mathematica soc",
      "arc disjoint spanning mixed arborescences",
      "tuttes theorem",
      "arc-disjoint arborescences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}