{
  "id": "2003.07943",
  "version": "v1",
  "published": "2020-03-17T21:06:42.000Z",
  "updated": "2020-03-17T21:06:42.000Z",
  "title": "Many cliques with few edges in a graph where the maximum degree is upper-bounded",
  "authors": [
    "Debsoumya Chakraborti",
    "Daqi Chen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Generalized Tur\\'an problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant of this problem where the number of edges is fixed instead of the number of vertices. In this paper, we determine the maximum number of cliques of a fixed order in a graph with fixed number of edges and bounded maximum degree, resolving a conjecture by Kirsch and Radcliffe. We also give a complete characterization of the extremal graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-17T21:06:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded maximum degree",
      "fixed number",
      "fixed order",
      "extremal combinatorics throughout",
      "generalized turan problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}