{
  "id": "1508.04620",
  "version": "v1",
  "published": "2015-08-19T12:43:32.000Z",
  "updated": "2015-08-19T12:43:32.000Z",
  "title": "Nowhere-zero 9-flows in 3-edge-connected signed graphs",
  "authors": [
    "Fan Yang",
    "Sanming Zhou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A signed graph is a graph with a positive or negative sign on each edge. Regarding each edge as two half edges, an orientation of a signed graph is an assignment of a direction to each of its half edges such that the two half edges of a positive edge receive the same direction and that of a negative edge receive opposite directions. A signed graph with such an orientation is called a bidirected graph. A nowhere-zero $k$-flow of a bidirected graph is an assignment of an integer from $\\{-(k-1), \\ldots, -1, 1, \\ldots, (k-1)\\}$ to each of its half edges such that Kirchhoff's law is respected, that is, the total incoming flow is equal to the total outgoing flow at each vertex. A signed graph is said to admit a nowhere-zero $k$-flow if it has an orientation such that the corresponding bidirected graph admits a nowhere-zero $k$-flow. It was conjectured by Bouchet that every signed graph admitting a nowhere-zero $k$-flow for some integer $k \\ge 2$ admits a nowhere-zero 6-flow. In this paper we prove that every $3$-edge-connected signed graph admitting a nowhere-zero $k$-flow for some $k$ admits a nowhere-zero $9$-flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-19T12:43:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C21",
      "05C22"
    ],
    "keywords": [
      "nowhere-zero",
      "half edges",
      "bidirected graph",
      "negative edge receive opposite directions",
      "orientation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150804620Y"
    }
  }
}