English

On independent sets in hypergraphs

Combinatorics 2011-06-17 v1

Abstract

The independence number of a hypergraph H is the size of a largest set of vertices containing no edge of H. In this paper, we prove new sharp bounds on the independence number of n-vertex (r+1)-uniform hypergraphs in which every r-element set is contained in at most d edges, where 0 < d < n/(log n)^{3r^2}. Our relatively short proof extends a method due to Shearer. We give an application to hypergraph Ramsey numbers involving independent neighborhoods.

Keywords

Cite

@article{arxiv.1106.3098,
  title  = {On independent sets in hypergraphs},
  author = {Alexander Kostochka and Dhruv Mubayi and Jacques Versatraete},
  journal= {arXiv preprint arXiv:1106.3098},
  year   = {2011}
}
R2 v1 2026-06-21T18:23:05.270Z