Math
Four colours for any map
Colour generated planar maps, inspect their adjacency graphs and compare greedy choices with a constrained backtracking search.
Try this
The map is a clipped Voronoi diagram; neighbours share an edge, not just a corner. Compare greedy colouring with saturation-ordered backtracking. Try a budget of two or three colours. The four-colour theorem concerns planar maps; this search demonstrates examples.
Equations used in the module
Equations Adjacent regions must have different colours Voronoi neighbours share a line segment of positive length A planar map admits a proper colouring with at most four colours Backtracking chooses a high-saturation vertex, tries a colour and retreats on failure
