The paper computes the exact Turán number ex(n, F5(f3;t)) for the blow-up of f3 in F5 and shows exponentially many extremal constructions, plus general bounds and exact values for other blow-ups including F_sim(t).
Geneson, A Generalization of the K˝ ov´ ari–S´ os–Tur´ an Theorem,Integers: Electronic Journal of Combinatorial Number Theory21(2021)
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On the Tur\'an number of blow-ups of $\mathcal{F}_5$
The paper computes the exact Turán number ex(n, F5(f3;t)) for the blow-up of f3 in F5 and shows exponentially many extremal constructions, plus general bounds and exact values for other blow-ups including F_sim(t).