On some extremal problems on r-graphs
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Denote by G^(^r^)(n;k) an r-graph of n vertices and kr-tuples. Turan's classical problem states: Determine the smallest integer @?(n;r,l) so that every G^(^r^)(n;@?(n;r,l)) contains a K^(^r^)(l). Turan determined @?(n;r,l) for r = 2, but nothing is known for r > 2. Put lim"n"="-@?(n;r,l)(nr)= c"r","l. The values of c"r","l are not known for r > 2. I prove that to every e > 0 and integer t there is an n"0 = n"0(t,@e) so that every G(^r)(n;[(c"r","l+@e)(nR)]) has lt vertices x"t(^j), l=
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