{
  "id": "1312.0407",
  "version": "v1",
  "published": "2013-12-02T10:48:47.000Z",
  "updated": "2013-12-02T10:48:47.000Z",
  "title": "Independence and Matching Number in Graphs with Maximum Degree 4",
  "authors": [
    "Felix Joos"
  ],
  "comment": "9 pages",
  "journal": "Discrete Math. 323 (2014) 1-6",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that $\\frac{7}{4}\\alpha(G)+\\beta(G)\\geq n(G)$ and $\\alpha(G)+\\frac{3}{2}\\beta(G)\\geq n(G)$ for every triangle-free graph $G$ with maximum degree at most $4$, where $\\alpha(G)$ is the independence number and $\\beta(G)$ is the matching number of $G$, respectively. These results are sharp for a graph on $13$ vertices. Furthermore we show $\\chi(G)\\leq \\frac{7}{4}\\omega(G)$ for $\\{3K_1,K_1\\cup K_5\\}$-free graphs, where $\\chi(G)$ is the chromatic number and $\\omega(G)$ is the clique number of $G$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-02T10:48:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum degree",
      "matching number",
      "triangle-free graph",
      "clique number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0407J"
    }
  }
}