{
  "id": "math/0607172",
  "version": "v1",
  "published": "2006-07-06T18:03:51.000Z",
  "updated": "2006-07-06T18:03:51.000Z",
  "title": "Simple and Direct Proof of MacLane's Planarity Criterion",
  "authors": [
    "Alexander Kelmans"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a simple proof of MacLane's algebraic planarity criterion for graphs. This proof does not use any other known planarity criteria. Keywords: graph, planarity, cycle space, a simple basis of a graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-06T18:03:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "maclanes planarity criterion",
      "direct proof",
      "maclanes algebraic planarity criterion",
      "simple proof",
      "cycle space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7172K"
    }
  }
}