Simulated annealing is a very successful heuristic for various problems in combinatorial
optimization. In this paper an application of simulated annealing to the 3-colouring problem
is considered. In contrast to many good empirical results we will show for a certain class of
graphs that the expected first hitting time of a proper colouring, given an arbitrary cooling
scheme, is of exponential size.
These results are complementary to those in [13], where we prove the convergence of
simulated annealing to an optimal solution in exponential time.