MathDB
2018 PAMO Shortlist: Colouring regions created by lines in a plane

Source: 2018 Pan-African Shortlist - C5

May 7, 2019
combinatoricsGraph coloring

Problem Statement

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