Let $G$ be a graph with $n$ vertices such that every induced subgraph on $\ge \lfloor n/2\rfloor$ vertices has more than $n^2/50$ edges. Must $G$ contain a triangle?

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

This is a famous open problem of Erdős and Rousseau (often called the **“sparse half” conjecture**). It asks exactly whether your condition forces a triangle. ([Erdős Problems][1])

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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