{
  "id": "1411.6668",
  "version": "v1",
  "published": "2014-11-24T22:13:31.000Z",
  "updated": "2014-11-24T22:13:31.000Z",
  "title": "Density of 5/2-critical graphs",
  "authors": [
    "Zdenek Dvorak",
    "Luke Postle"
  ],
  "comment": "26 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently, homomorphism to C_5), but every proper subgraph of G has one. We prove that every 5/2-critical graph on n>=4 vertices has at least (5n-2)/4 edges, and list all 5/2-critical graphs achieving this bound. This implies that every planar or projective-planar graph of girth at least 10 is 5/2-colorable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-24T22:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "G.2.2"
    ],
    "keywords": [
      "proper subgraph",
      "projective-planar graph",
      "homomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}