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arXiv · 1106.3098

On independent sets in hypergraphs

Alexander Kostochka·Dhruv Mubayi·Jacques Versatraete
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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.

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Alexander Kostochka, Dhruv Mubayi, Jacques Versatraete. 2011-06-15. On independent sets in hypergraphs. https://arxiv.org/abs/1106.3098

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