Colourings

A colouring is a function that assigns a colour (often represented by numbers or symbols) to each element of a set, such as the points of a geometric figure. Colourings are used to study patterns, avoid certain configurations, or prove the existence of certain arrangements.

Important properties

• Colourings can be used to avoid monochromatic (all one colour) structures, such as lines or triangles.

• The minimum number of colours needed to avoid a certain configuration is called the chromatic number.

• Colourings are often used in proofs by contradiction, especially in Ramsey-type problems.