{
  "id": "math/0408363",
  "version": "v1",
  "published": "2004-08-26T06:41:31.000Z",
  "updated": "2004-08-26T06:41:31.000Z",
  "title": "Three Colorability of an Arrangement Graph of Great Circles",
  "authors": [
    "I. Cahit"
  ],
  "comment": "6 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Stan Wagon asked the following in 2000. Is every zonohedron face 3-colorable when viewed as a planar map? An equivalent question, under a different guise, is the following: is the arrangement graph of great circles on the sphere always vertex 3-colorable? (The arrangement graph has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points.) Assume that no three circles meet at a point, so that this arrangement graph is 4-regular. In this note we have shown that all arrangement graphs defined as above are 3-colorable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-26T06:41:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "arrangement graph",
      "great circles",
      "colorability",
      "intersection point",
      "equivalent question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8363C"
    }
  }
}