Learners replace each region with a vertex and join vertices whose regions share a border. This transforms a visual map-colouring problem into a graph-colouring problem that can be explored systematically.

This lesson introduces:

• turning a map into an adjacency graph;
• proper colourings;
• the chromatic number of a graph;
• finding colourings that use as few colours as possible;
• explaining why fewer colours cannot work;
• the statement and history of the Four Colour Theorem;
• applications such as timetable and scheduling problems.

The download includes the main lesson and a supplementary examples booklet with further problems, answer checks and model solutions.

Suitable for learners aged 10 and over. No previous experience of graph colouring is required.

This is Lesson 5 of the six-part Beyond Curriculum: Graphs course.

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