Anagram-Free Graph Colouring
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An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al.[Random Structures & Algorithms 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 $k$-anagram-free colouring.
2011 ◽
Vol Vol. 13 no. 2
(Graph and Algorithms)
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1986 ◽
Vol 100
(2)
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pp. 303-317
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2020 ◽
Vol 12
(02)
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pp. 2050021
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2014 ◽
Vol 2014
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pp. 1-4
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2017 ◽
Vol 09
(02)
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pp. 1750024
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