Let f r (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 Erdos, Frankl and Rödl, we partially resolve a problem raised by Brown, Erdos and Sós in 1973, by showing that for any fixed 2≤k<r, we have n k-o(1) < fr (n, 3(r - k) + k + 1, 3) = o(n k).
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Computational Mathematics