$2\times n$ Grids have Unbounded Anagram-Free Chromatic Number

Saman Bazarghani; Paz Carmi; Vida Dujmović; Pat Morin

$2\times n$ Grids have Unbounded Anagram-Free Chromatic Number

Combinatorics 2021-05-06 v1 Discrete Mathematics

Authors: Saman Bazarghani , Paz Carmi , Vida Dujmović , Pat Morin

Abstract

We show that anagram-free vertex colouring a $2\times n$ square grid requires a number of colours that increases with $n$ . This answers an open question in Wilson's thesis and shows that even graphs of pathwidth $2$ do not have anagram-free colourings with a bounded number of colours.

Keywords

anagram-free coloring grid graph chromatic number pathwidth vertex coloring

Cite

@article{arxiv.2105.01916,
  title  = {$2\times n$ Grids have Unbounded Anagram-Free Chromatic Number},
  author = {Saman Bazarghani and Paz Carmi and Vida Dujmović and Pat Morin},
  journal= {arXiv preprint arXiv:2105.01916},
  year   = {2021}
}

Comments

11.3 pages, 6 figures

Related papers

View all related →