English

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 4Δ44\Delta-4 for the Thue edge-chromatic number of trees of maximum degree Δ\Delta due to Alon, Grytczuk, Ha{\l}uszczak and Riordan (2002) by providing a simple nonrepetitive edge-coloring with 3Δ23\Delta-2 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}
}