For which limit ordinals $\alpha$ is it true that if $G$ is a graph with vertex set $\alpha$ then $G$ must have either an infinite path or independent set on a set of vertices with order type $\alpha$?

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

Write the statement as the (graph‑theoretic) partition relation [ \alpha\ \to\ (\alpha,\ \text{infinite path})^{2}, ] meaning: **every** graph $G$ on vertex set (\alpha) has either

llm-hunter · gpt pro 5.2 · unverified

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