High Quality Content by WIKIPEDIA articles! In the mathematical area of graph theory, the Thue number of a graph is a variation of the chromatic index, defined by Alon et al. (2002) and named by them after mathematician Axel Thue, who studied the squarefree words used to define this number. Alon et al. define a nonrepetitive coloring of a graph to be an assignment of colors to the edges of the graph, such that there does not exist any even-length simple path in the graph in which the colors of the edges in the first half of the path form the same sequence as the colors of the edges in the second half of the path. The Thue number of a graph is the minimum number of colors needed in any nonrepetitive coloring.

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