{
  "id": "2207.09659",
  "version": "v1",
  "published": "2022-07-20T05:29:39.000Z",
  "updated": "2022-07-20T05:29:39.000Z",
  "title": "Decomposition of triangle-free planar graphs",
  "authors": [
    "Rongxing Xu",
    "Xuding Zhu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A decomposition of a graph $G$ is a family of subgraphs of $G$ whose edge sets form a partition of $E(G)$. In this paper, we prove that every triangle-free planar graph $G$ can be decomposed into a $2$-degenerate graph and a matching. Consequently, every triangle-free planar graph $G$ has a matching $M$ such that $G-M$ is online 3-DP-colorable. This strengthens an earlier result in [R. \\v{S}krekovski, {\\em A Gr\\\"{o}tzsch-Type Theorem for List Colourings with Impropriety One}, Combin. Prob. Comput. 8 (1999), 493-507] that every triangle-free planar graph is $1$-defective $3$-choosable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-20T05:29:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangle-free planar graph",
      "decomposition",
      "edge sets form",
      "degenerate graph",
      "earlier result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}