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Jun 15, 2023 at 12:03 comment added Yevgeny Levanzov Indeed, thanks!
Jun 15, 2023 at 11:17 comment added Tony Huynh You're right. I edited the answer. It follows from a result of Alon and Shikhelman.
Jun 15, 2023 at 11:17 history edited Tony Huynh CC BY-SA 4.0
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Jun 15, 2023 at 9:32 comment added Yevgeny Levanzov This is not quite right: the fact that $G$ has $n^{r-\varepsilon}$ copies of $K_r$ does not imply that at most $O(n^\varepsilon)$ $r$-subsets are not cliques, as the $-\varepsilon$ is in the exponent, thus $n^{r-\varepsilon} + x = \Theta(n^r)$ gives $x \approx n^{r-\varepsilon} \cdot (n^\varepsilon - 1)$ $r$-subsets which are not cliques.
Jun 14, 2023 at 17:52 vote accept Yevgeny Levanzov
Jun 14, 2023 at 17:50 history edited Tony Huynh CC BY-SA 4.0
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Jun 14, 2023 at 17:44 history answered Tony Huynh CC BY-SA 4.0