The complexity of nonrepetitive coloring Original Research Article

A coloring of a graph is nonrepetitive if the graph contains no path that has a color pattern of the form image (where image 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 image up to a fixed length image of image.