graph colouring application
A constraint-satisfaction problem often used as a test case in research, which also turns out to be equivalent to certain real-world problems (e.g. register allocation). Given a connected graph and a fixed number of colours, the problem is to assign a colour to each node, subject to the constraint that any two connected nodes cannot be assigned the same colour. This is an example of an NP-complete problem.
See also four colour map theorem.