Kruft's terminal-set conjecture

Let $G$ be a graph. A set $S\subseteq V(G)$ is a terminal set if $S$ is a general position set of $G$ and adding any vertex $u\in V(G)-S$ to $S$ creates three-in-a-line with $u$ as an endpoint. Kruft's conjecture. Every graph has a terminal set.

Terminal sets correspond to maximal general position sets contained in a layer of a Cartesian product. The conjecture is known for graphs of diameter at most three, cographs, and chordal graphs, but remains open in general.