Many holes but no large one: maximizing $k$-holes while forbidding $(k+1)$-holes

Martin Andričík, Alica Dományová, Adam Džavoronok +2

We study the maximal number $m_{k,\ell ,n}$ of empty convex $k$-gons ($k$-holes) determined by an $n$-point set in the plane in general position that contains no empty convex $\ell~…