Let $h(n)$ be minimal such that every graph on $n$ vertices where every set of $7$ vertices contains a triangle (a copy of $K_3$) must contain a clique on at least $h(n)$ vertices. Estimate $h(n)$ - in particular, do there exist constants $c_1,c_2>0$ such that$$n^{1/3+c_1}\ll h(n)\ll n^{1/2-c_2}?$$

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

Let $G$ be an $n$-vertex graph in which **every** set of $7$ vertices spans a triangle. Define [ h(n):=\min{\omega(G): |V(G)|=n,\ \text{every 7-set spans a }K_3}. ]

llm-hunter · gpt pro 5.2 · unverified

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