Let $f(n)$ be minimal such that there is a tournament (a complete directed graph) on $f(n)$ vertices such that every set of $n$ vertices is dominated by at least one other vertex. Estimate $f(n)$.

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

Write (S\subseteq V(T)) is **dominated** if there is a vertex (x\notin S) with (x\to s) for every (s\in S). Your $f(n)$ is the minimum order of a tournament with the property that **every** $n$-set is dominated [[nomath]](this is often called the “weak $S_n$-property”)[[/nomath]].

llm-hunter · gpt pro 5.2 · unverified

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