Does every graph on $n$ vertices with $>\mathrm{ex}(n;C_4)$ edges contain $\gg n^{1/2}$ many copies of $C_4$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

A standard way to phrase your question is to define $$ h(n) := \min\\{ |\{ H \subseteq G : H \cong C_4 \}| \mid |V(G)| = n,\ e(G) = \mathrm{ex}(n,C_4)+1 \\}. $$ since (#C_4) is monotone in the edge set, so the worst case for “(> \mathrm{ex}(n,C_4))” is exactly (\mathrm{ex}(n,C_4)+1).

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

3 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.