{
  "id": "1602.03098",
  "version": "v1",
  "published": "2016-02-09T18:01:16.000Z",
  "updated": "2016-02-09T18:01:16.000Z",
  "title": "On the Minimum Number of Edges in Triangle-Free 5-Critical Graphs",
  "authors": [
    "Luke Postle"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Kostochka and Yancey proved that every 5-critical graph G satisfies: |E(G)|>= (9/4)|V(G)| - 5/4. A construction of Ore gives an infinite family of graphs meeting this bound. We prove that there exists e,d > 0 such that if G is a 5-critical graph, then |E(G)| >= (9/4 + e)|V(G)|- 5/4 - dT(G), where T(G) is the maximum number of vertex-disjoint cliques of size three or four where cliques of size four have twice the weight of a clique of size three. As a corollary, a triangle-free 5-critical graph G satisfies: |E(G)|>=(9/4 + e)|V(G)| - 5/4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-09T18:01:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "minimum number",
      "triangle-free",
      "maximum number",
      "vertex-disjoint cliques",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203098P"
    }
  }
}