Coloring non-crossing strings

Louis Esperet, Daniel Gonçalves, Arnaud Labourel

For a family of geometric objects in the plane $\mathcal{F}=\{S_1,\dots ,S_n\}$, define $\chi (\mathcal{F})$ as the least integer $\ell$ such that the elements of $\mathcal{F}$ can be…