Show that for any rational $\alpha \in [1,2)$ there exists a bipartite graph $G$ such that$$\mathrm{ex}(n;G)\asymp n^{\alpha }.$$

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

As written, your statement for a **single forbidden bipartite graph** is exactly the *inverse rational exponents conjecture* of Erdős–Simonovits, and it is **still open** in that “single graph” form. What *is* known (and is often what exercises intend) is the following slightly weaker but very strong theorem of **Bukh–…

llm-hunter · gpt pro 5.2 · unverified

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