The Free On-line Dictionary of Computing (30 December 2018):

graph colouring
graph coloring

    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.