2 × n grids have unbounded anagram-free chromatic number∗

Saman Bazargani; Paz Carmi; Vida Dujmović; Pat Morin

doi:10.37236/10411

2 × n grids have unbounded anagram-free chromatic number^∗

Saman Bazargani, Paz Carmi, Vida Dujmović, Pat Morin

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	3.43
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	3
DOIs	https://doi.org/10.37236/10411
State	Published - 1 Jan 2022

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/10411

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

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2 × n grids have unbounded anagram-free chromatic number^∗

Abstract

ASJC Scopus subject areas

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