{
  "id": "2205.07498",
  "version": "v1",
  "published": "2022-05-16T08:14:11.000Z",
  "updated": "2022-05-16T08:14:11.000Z",
  "title": "On density of $Z_3$-flow-critical graphs",
  "authors": [
    "Zdeněk Dvořák",
    "Bojan Mohar"
  ],
  "comment": "22 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an abelian group $\\Gamma$, a graph $G$ is said to be $\\Gamma$-flow-critical if $G$ does not admit a nowhere-zero $\\Gamma$-flow, but for each edge $e\\in E(G)$, the contraction $G/e$ has a nowhere-zero $\\Gamma$-flow. A bound on the density of $Z_3$-flow-critical graphs drawn on a fixed surface is obtained, generalizing the bound on the density of 4-critical graphs by Kostochka and Yancey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-16T08:14:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C21"
    ],
    "keywords": [
      "abelian group",
      "nowhere-zero",
      "flow-critical graphs drawn",
      "contraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}