Geodesic
Nonrepetitive edge-colorings of trees
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1.

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A repetition is a sequence of symbols in which the first half is the same as the second half. An edge-coloring of a graph is repetition-free or nonrepetitive if there is no path with a color pattern that is a repetition. The minimum number of colors so that a graph has a nonrepetitive edge-coloring is called its Thue edge-chromatic number. We improve on the best known general upper bound of $4\Delta-4$ for the Thue edge-chromatic number of trees of maximum degree $\Delta$ due to Alon, Grytczuk, Ha{\l}uszczak and Riordan (2002) by providing a simple nonrepetitive edge-coloring with $3\Delta-2$ colors. 
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     author = {K\"undgen, A. and Talbot, T.},
     title = {Nonrepetitive edge-colorings of trees},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2017-2018},
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     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-18/}
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Kündgen, A.; Talbot, T. Nonrepetitive edge-colorings of trees. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 1. doi : 10.23638/DMTCS-19-1-18. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-1-18/

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