Discoveries / combinatorics

The Kára–Pór–Wood Big-Line-Big-Clique Conjecture: Four Collinear Points or a Six-Clique

The big-line-big-clique conjecture of Kára, Pór and Wood asserts that for all $k, \ell$ there is an $n$ such that every finite point set of at least $n$ points contains $\ell$ collinear points or $k$ points that pairwise see each other. True for $\ell = 4$, $k = 6$, the first case left open: every finite point set of size at least $10^{11055931}$ has four collinear points or six pairwise visible points.