Kára–Pór–Wood Big-Line–Big-Clique Conjecture

Let $A\subset\mathbb{R}^2$ be a finite planar point set. Two points of $A$ are visible if the open segment between them contains no other point of $A$; a mutually visible subset is a set whose pairs are all visible. Big-Line–Big-Clique Conjecture. For every pair of integers $k,\ell\ge 2$ there is $n_0(k,\ell)$ such that every set $A\subset\mathbb{R}^2$ with $|A|\ge n_0(k,\ell)$ contains either $k$ collinear points or $\ell$ mutually visible points. This is a Ramsey-type problem for planar point sets. The paper proves the conclusion in several structured regimes, including point sets on fixed irreducible algebraic curves, but the full conjecture remains open.