Let $G$ be a graph with chromatic number $k$ containing no $K_k$. If $a,b\ge 2$ and $a+b=k+1$ then must there exist two disjoint subgraphs of $G$ with chromatic numbers $\ge a$ and $\ge b$ respectively?

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

This is **exactly the Erdős–Lovász Tihany conjecture** [[nomath]](sometimes phrased as “$(a,b)$-splittable”)[[/nomath]]. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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