{
  "id": "1706.03092",
  "version": "v1",
  "published": "2017-06-09T18:57:40.000Z",
  "updated": "2017-06-09T18:57:40.000Z",
  "title": "Finding Balance: Split Graphs and Related Classes",
  "authors": [
    "Karen L. Collins",
    "Ann N. Trenk"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following interesting counting fact: unlabeled, unbalanced split graphs on $n$ vertices can be placed into a bijection with all unlabeled split graphs on $n-1$ or fewer vertices. In this paper we translate these concepts and the theorem to different combinatorial settings: minimal set covers, bipartite graphs with a distinguished block and posets of height one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-09T18:57:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C17",
      "06A07"
    ],
    "keywords": [
      "related classes",
      "finding balance",
      "minimal set covers",
      "unbalanced split graphs",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}