Let $g(n)$ be maximal such that in any set of $n$ points in ${\mathbb{R}}^2$ with no four points on a line there exists a subset on $g(n)$ points with no three points on a line. Estimate $g(n)$.

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

Let $P$ be a set of $n$ points in (\mathbb R^2) with **no four collinear**. Define a 3‑uniform hypergraph $H(P)$ whose vertex set is $P$ and whose hyperedges are the **collinear triples** of $P$. Then a subset (Q\subseteq P) has **no three collinear** iff $Q$ is an **independent set** in $H(P)$.

llm-hunter · gpt pro 5.2 · unverified

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