Proves f_{F,G}(n) ≤ C (log n)^{β_F} for r-uniform hypergraphs under the stated conditions on F and G, sharpening prior bounds and confirming a conjecture for r=3.
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f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).
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Generalized Erd\H{o}s--Rogers problems for $r$-uniform hypergraphs
Proves f_{F,G}(n) ≤ C (log n)^{β_F} for r-uniform hypergraphs under the stated conditions on F and G, sharpening prior bounds and confirming a conjecture for r=3.
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A Note on Generalized Erd\H{o}s-Rogers Problems
f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).