{
  "id": "2109.08193",
  "version": "v1",
  "published": "2021-09-16T19:21:18.000Z",
  "updated": "2021-09-16T19:21:18.000Z",
  "title": "Shadow of Hypergraphs with Bounded Degree",
  "authors": [
    "Attila Jung"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the size of the shadow of $k$-uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a function of the degree bound and $k$. We show that cliques are extremal for a long range of degree bounds, but not for every bound. We give a general, but not sharp lower bound on the shadow ratio and show, that sometimes we can get extremal hypergraphs by deleting disjoint maximal matchings from a clique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-16T19:21:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65",
      "05C35"
    ],
    "keywords": [
      "bounded degree",
      "degree bound",
      "deleting disjoint maximal matchings",
      "sharp lower bound",
      "uniform hypergraphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}