## Nonrepetitive colorings of graphs – a survey.(English)Zbl 1139.05020

Summary: A vertex coloring $$f$$ of a graph $$G$$ is nonrepetitive if there are no integer $$r\geq 1$$ and a simple path $$\nu_1,\dots,\nu_{2r}$$ in $$G$$ such that $$f(\nu_i)= f(\nu_{r+i})$$ for all $$i=1,\dots,r$$. This notion is a graph-theoretic variant of nonrepetitive sequences of Thue. The paper surveys problems and results on this topic.

### MSC:

 05C15 Coloring of graphs and hypergraphs
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### References:

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