• Corpus ID: 5489770

The complexity of nonrepetitive edge coloring of graphs

@article{Manin2007TheCO,
  title={The complexity of nonrepetitive edge coloring of graphs},
  author={Fedor Manin},
  journal={ArXiv},
  year={2007},
  volume={abs/0709.4497}
}
A squarefree word is a sequence $w$ of symbols such that there are no strings $x, y$, and $z$ for which $w=xyyz$. A nonrepetitive coloring of a graph is an edge coloring in which the sequence of colors along any open path is squarefree. We show that determining whether a graph $G$ has a nonrepetitive $k$-coloring is $\Sigma_2^p$-complete. When we restrict to paths of lengths at most $n$, the problem becomes NP-complete for fixed $n$. 
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The complexity of nonrepetitive coloring
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