On the intersections of systems of curves
Let \(i_m(n)\) be the minimum number of intersections in a family of \(n\) simple closed curves whose members have pairwise at least one and less than \(m\) common points, where no point of the plane is in more than two members of the family. It is proved that \(\lim_{n\to\infty}\left(i_m(n)\left/\right.\left(\begin{smallmatrix} n\\ 2\end{smallmatrix}\right)\right)= 2\). The author asks for a characaterization of simple closed curves \(C\) such that the maximum number of intersections between two curves similar to \(C\) is finite.
scientific article; zbMATH DE number 1347236