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On an extremal hypergraph problem of Brown, Erdős and Sós. (English) Zbl 1121.05079
Summary: 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 I. Z. Ruzsa and E. Szemerédi [Combinatorics, Keszthely 1976, Colloq. Math. Soc. Janos Bolyai 18, 939–945 (1978; Zbl 0393.05031)] and of P. Erdős, P. Frankl and V. Rödl [Graphs Comb. 2, 113–121 (1986; Zbl 0593.05038)] we partially resolve a problem raised by W. G. Brown, P. Erdős and V. T. Sós [Period. Math. Hung. 3, 221–228 (1973; Zbl 0269.05111)], by showing that for any fixed $$2\leq k<r$$, we have $n^{k-o(1)}<f_r(n,3(r-k)+k+1,3)=o(n^k).$

##### MSC:
 05C65 Hypergraphs 05D99 Extremal combinatorics
hypergraph
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