$2\times n$ Grids have Unbounded Anagram-Free Chromatic Number
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Published:2022-08-26
Issue:3
Volume:29
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Bazarghani Saman,Carmi Paz,Dujmović Vida,Morin Pat
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 there are even graphs of pathwidth $2$ that do not have anagram-free colourings with a bounded number of colours.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics