## Kündgen, A. and Talbot, T. - Nonrepetitive edge-colorings of trees

dmtcs:2651 - Discrete Mathematics & Theoretical Computer Science, June 27, 2017, Vol. 19 no. 1 - https://doi.org/10.23638/DMTCS-19-1-18
Nonrepetitive edge-colorings of trees

Authors: Kündgen, A. and Talbot, T.

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.

Volume: Vol. 19 no. 1
Section: Graph Theory
Published on: June 27, 2017
Submitted on: June 20, 2017
Keywords: Mathematics - Combinatorics,05C05, 05C15, 68R15