{
  "id": "1910.05058",
  "version": "v1",
  "published": "2019-10-11T10:00:34.000Z",
  "updated": "2019-10-11T10:00:34.000Z",
  "title": "Spanning Triangle-trees and Flows of Graphs",
  "authors": [
    "Jiaao Li",
    "Xueliang Li",
    "Meiling Wang"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study the flow-property of graphs containing a spanning triangle-tree. Our main results provide a structure characterization of graphs with a spanning triangle-tree admitting a nowhere-zero $3$-flow. All these graphs without nowhere-zero $3$-flows are constructed from $K_4$ by a so-called bull-growing operation. This generalizes a result of Fan et al. in 2008 on triangularly-connected graphs and particularly shows that every $4$-edge-connected graph with a spanning triangle-tree has a nowhere-zero $3$-flow. A well-known classical theorem of Jaeger in 1979 shows that every graph with two edge-disjoint spanning trees admits a nowhere-zero $4$-flow. We prove that every graph with two edge-disjoint spanning triangle-trees has a flow strictly less than $3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-11T10:00:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C21",
      "05C40",
      "05C05"
    ],
    "keywords": [
      "nowhere-zero",
      "edge-disjoint spanning trees admits",
      "main results",
      "structure characterization",
      "edge-disjoint spanning triangle-trees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}