Nonrepetitive edge-colorings of trees
Combinatorics
2023-06-22 v2
Abstract
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 for the Thue edge-chromatic number of trees of maximum degree due to Alon, Grytczuk, Ha{\l}uszczak and Riordan (2002) by providing a simple nonrepetitive edge-coloring with colors.
Keywords
Cite
@article{arxiv.1701.04227,
title = {Nonrepetitive edge-colorings of trees},
author = {A. Kündgen and T. Talbot},
journal= {arXiv preprint arXiv:1701.04227},
year = {2023}
}