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}
}