{
  "id": "1803.03393",
  "version": "v1",
  "published": "2018-03-09T06:29:46.000Z",
  "updated": "2018-03-09T06:29:46.000Z",
  "title": "New results on $k$-independence of hypergraphs",
  "authors": [
    "Lei Zhang",
    "An Chang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $H=(V,E)$ be an $s$-uniform hypergraph of order $n$ and $k\\geq 0$ be an integer. A $k$-independent set $S\\subseteq H$ is a set of vertices such that the maximum degree in the hypergraph induced by $S$ is at most $k$. Denoted by $\\alpha_k(H)$ the maximum cardinality of the $k$-independent set of $H$. In this paper, we first give a lower bound of $\\alpha_k(H)$ by the maximum degree of $H$. Furthermore, we prove that $\\alpha_k(H)\\geq \\frac{s(k+1)n}{2d+s(k+1)}$ where $d$ is average degree of $H$, and $k\\geq 0$ is an integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-09T06:29:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "05C69"
    ],
    "keywords": [
      "maximum degree",
      "independence",
      "independent set",
      "average degree",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}