{
  "id": "1004.0582",
  "version": "v1",
  "published": "2010-04-05T07:36:45.000Z",
  "updated": "2010-04-05T07:36:45.000Z",
  "title": "Every planar graph without adjacent short cycles is 3-colorable",
  "authors": [
    "Tao Wang"
  ],
  "comment": "14 pages, 16 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Two cycles are {\\em adjacent} if they have an edge in common. Suppose that $G$ is a planar graph, for any two adjacent cycles $C_{1}$ and $C_{2}$, we have $|C_{1}| + |C_{2}| \\geq 11$, in particular, when $|C_{1}| = 5$, $|C_{2}| \\geq 7$. We show that the graph $G$ is 3-colorable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-05T07:36:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "adjacent short cycles",
      "planar graph",
      "adjacent cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.0582W"
    }
  }
}