{
  "id": "2008.12975",
  "version": "v1",
  "published": "2020-08-29T13:23:18.000Z",
  "updated": "2020-08-29T13:23:18.000Z",
  "title": "Family sizes for complete multipartite graphs",
  "authors": [
    "Danielle Gregg",
    "Thomas W. Mattman",
    "Zachary Porat",
    "George Todd"
  ],
  "comment": "18 pages, 14 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Inspired by a question of Goldberg et al., we investigate the size of the $\\nabla Y$ family for a complete multipartite graph. Aside from three families, which appear to grow exponentially, these families stabilize: after a certain point, increasing the number of vertices in the largest part does not change family size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-29T13:23:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15",
      "05C35"
    ],
    "keywords": [
      "complete multipartite graph",
      "family size",
      "largest part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}