Anagram-free Graph Colouring
Abstract
An anagram is a word of the form where is a non-empty word and is a permutation of . We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and -anagram-free colouring.
Keywords
Cite
@article{arxiv.1607.01117,
title = {Anagram-free Graph Colouring},
author = {Tim E. Wilson and David R. Wood},
journal= {arXiv preprint arXiv:1607.01117},
year = {2019}
}
Comments
Version 2: Changed 'abelian square' to 'anagram' for consistency with 'Anagram-free colourings of graphs' by Kam\v{c}ev, {\L}uczak, and Sudakov. Minor changes based on referee feedback