  A colouring of a graph is "nonrepetitive" if for every path of even order,
the sequence of colours on the first half of the path is different from the
sequence of colours on the second half. We show that planar graphs have
nonrepetitive colourings with a bounded number of colours, thus proving a
conjecture of Alon, Grytczuk, Haluszczak and Riordan (2002). We also generalise
this result for graphs of bounded Euler genus, graphs excluding a fixed minor,
and graphs excluding a fixed topological minor.
