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.