Arrangements of pseudolines are a widely studied generalization of line arrangements. They are defined as a finite family of infinite curves in the Euclidean plane, any two of which intersect at exactly one point. One can state various related coloring problems depending on the number $n$ of pseudolines. In this article, we show that $n$ colors are sufficient for coloring the crossings avoiding twice the same color on the boundary of any cell, or, alternatively, avoiding twice the same color along any pseudoline. We also study the problem of coloring the pseudolines avoiding monochromatic crossings.

翻译：伪线排列是直线排列的一种广泛研究的推广形式，定义为欧几里得平面中无限曲线的有限族，其中任意两条曲线恰好相交于一点。根据伪线数量 $n$，可以提出多种相关的着色问题。本文证明，在避免任何单元格边界上出现相同颜色两次（或等价地，避免任何伪线上出现相同颜色两次）的条件下，$n$种颜色足以对交叉点进行着色。我们还研究了避免单色交叉的伪线着色问题。