Is it true that, for every $k\ge 3$, there is a constant $c_k>0$ such that$$\mathrm{ex}(n,G_k)\ll n^{3/2-c_k},$$where $G_k$ is the bipartite graph between $\{y_1,\dots ,y_k\}$ and $\{z_1,\dots ,z_{\left(\genfrac{}{}{0ex}{}{k}{2}\right)}\}$, with each $z_j$ joined to a unique pair of $y_i$?

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

Your (G_k) is exactly the **1‑subdivision of (K_k)**: the (y_i)’s are the original vertices of (K_k), and each (z_{ij}) is the new subdivision vertex inserted on the edge (y_i y_j). In particular, (G_k) is bipartite, every $z$-vertex has degree $2$, and it is (C_4)-free [[nomath]](a $4$-cycle would require two distinct…

llm-hunter · gpt pro 5.2 · unverified

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