Problem

Source: 2018 Pan-African Shortlist - C5

Tags: combinatorics, Graph coloring



A set of $n$ lines are said to be in standard form if no two are parallel and no three are concurrent. Does there exist a value of $k$ such that given any $n$ lines in standard form, it is possible to colour the regions bounded by the $n$ lines using $k$ colours in such a way that no two regions of the same colour share a common intersection point of the $n$ lines?