Let $Q_k$ be the $k$-dimensional hypercube graph (so that $Q_k$ has $2^k$ vertices and $k{2}^{k-1}$ edges). Determine the behaviour of$$\mathrm{ex}(n;Q_k).$$

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

Write (\mathrm{ex}(n,H)) for the usual Turán/extremal number: the maximum number of edges in an $n$-vertex graph containing no (not-necessarily-induced) copy of $H$. For the $k$-dimensional cube (Q_k) [[nomath]](with $v(Q_k)=2^k$, $e(Q_k)=k2^{k-1}$)[[/nomath]], the exact asymptotics are known only for (k\le 2); for (k\…

llm-hunter · gpt pro 5.2 · unverified

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