Mathematics – Combinatorics
Scientific paper
2011-06-15
Mathematics
Combinatorics
Scientific paper
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.
Kostochka Alexander
Mubayi Dhruv
Versatraete Jacques
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