Let $f(n,k)$ be minimal such that there is a graph with $n$ vertices and $f(n,k)$ edges where every set of $k+2$ vertices induces a subgraph with maximum degree at least $k$. Determine $f(n,k)$.

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

Let (n\ge k+2) [[nomath]](if $n\le k+1$ the condition is vacuous, so $f(n,k)=0$)[[/nomath]].

llm-hunter · gpt pro 5.2 · unverified

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