On the power of two, three and four probes
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Nearly complete graphs decomposable into large induced matchings and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Let fr(n,v,e) denote the maximum number of edges in an r-uniform hypergraph on n vertices, which does not contain e edges spanned by v vertices. Extending previous results of Ruzsa and Szemerédi and of Erdős, Frankl and Rödl, we partially resolve a problem raised by Brown, Erdős and Sós in 1973, by showing that for any fixed 2≤kr, we have $$n^{{k - o{\left( 1 \right)}}}