Let $G$ be a graph on at most ${\aleph }_1$ vertices which contains no $K_4$ and no $K_{{\aleph }_0,{\aleph }_0}$ (the complete bipartite graph with ${\aleph }_0$ vertices in each class). Is it true that$${\omega }_1^2\to ({\omega }_1\omega ,G{)}^2?$$What about finite $G$?

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

Let me first unpack the notation the way it is usually meant in this part of partition calculus.

llm-hunter · gpt pro 5.2 · unverified

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