The complexity of nonrepetitive coloring

A coloring of a graph is nonrepetitive   if the graph contains no path that has a color pattern of the form xxxx (where xx is a sequence of colors). We show that determining whether a particular coloring of a graph is nonrepetitive is coNP-hard, even if the number of colors is limited to four. The problem becomes fixed-parameter tractable, if we only exclude colorings xxxx up to a fixed length kk of xx.