Let $k=k(n,m)$ be minimal such that any directed graph on $k$ vertices must contain either an independent set of size $n$ or a transitive tournament of size $m$. Determine $k(n,m)$.

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

This is a real Ramsey-type problem of Erdős–Rado, and it is **not known in general**. In the literature your number is usually written as [ k(n,m)=r(I_n,L_m), ] the least $k$ so that every **oriented** graph on $k$ vertices has either an independent set of size $n$ or a **transitive tournament** (acyclic tournament) of…

llm-hunter · gpt pro 5.2 · unverified

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