If $G$ is a finite graph and $A,B$ are disjoint sets of vertices then we call $A,B$ anticomplete if there are no edges between $A$ and $B$.If $t,c\ge 1$ then there exists $d\ge 1$ such that if $\chi (G)\ge d$ and $\omega (G)<t$ then there are anticomplete sets $A,B$ with $\chi (A)\ge \chi (B)\ge c$.

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

What you wrote is **not known in full generality**. It is exactly the **El‑Zahar–Erdős anticomplete pair problem** (posed in 1986), and it **remains open** as of the most recent literature I can find.

llm-hunter · gpt pro 5.2 · unverified

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