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- W2469043294 abstract "A sequence $S$ is called anagram-free if it contains no consecutive symbols $r_1 r_2dots r_k r_{k+1} dots r_{2k}$ such that $r_{k+1} dots r_{2k}$ is a permutation of the block $r_1 r_2dots r_k$. Answering a question of Erdős and Brown, Keranen constructed an infinite anagram-free sequence on four symbols. Motivated by the work of Alon, Grytczuk, Haluszczak and Riordan, we consider a natural generalisation of anagram-free sequences for graph colorings. A coloring of the vertices of a given graph $G$ is called anagram-free if the sequence of colors on any path in $G$ is anagram-free. We call the minimal number of colors needed for such a coloring the anagram-chromatic number of $G$. In this paper we study the anagram-chromatic number of several classes of graphs like trees, minor-free graphs and bounded-degree graphs. Surprisingly, we show that there are bounded-degree graphs (such as random regular graphs) in which anagrams cannot be avoided unless we basically give each vertex a separate color." @default.
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- W2469043294 date "2016-06-29" @default.
- W2469043294 modified "2023-09-27" @default.
- W2469043294 title "Anagram-free colorings of graphs" @default.
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