2 problems

3-decomposable optimality conjecture. For every $k$ and $n$, the class of $3$-decomposable sets contains optimal sets for both $E_{\leq k}(n)$ and $\overline{\operatorname{cr}}(n)$…

Let $P$ be an unrestricted point-set of $n$ points in the plane. Write $E_{\leq k}(P)$ for the number of edges of the geometric complete graph on $P$ incident to at most $k$ points…