{
  "id": "2208.08498",
  "version": "v1",
  "published": "2022-08-17T19:34:29.000Z",
  "updated": "2022-08-17T19:34:29.000Z",
  "title": "On $α$-excellent graphs",
  "authors": [
    "M. Dettlaff",
    "M. A. Henning",
    "J. Topp"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ is $\\alpha$-excellent if every vertex of $G$ is contained in some maximum independent set of $G$. In this paper, we characterize $\\alpha$-excellent bipartite graphs, $\\alpha$-excellent unicyclic graphs, $\\alpha$-excellent simplicial graphs, $\\alpha$-excellent chordal graphs, $\\alpha$-excellent block graphs, and we show that every generalized Petersen graph is $\\alpha$-excellent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-17T19:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "F.2.2"
    ],
    "keywords": [
      "excellent graphs",
      "maximum independent set",
      "excellent block graphs",
      "excellent bipartite graphs",
      "excellent chordal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}