A note on list-coloring powers of graphs

@article{Kosar2014ANO,
  title={A note on list-coloring powers of graphs},
  author={Nicholas Kosar and S{\'a}rka Petrickova and Benjamin Reiniger and Elyse Yeager},
  journal={Discrete Mathematics},
  year={2014},
  volume={332},
  pages={10-14}
}
Recently, Kim and Park have found an infinite family of graphs whose squares are not chromatic-choosable. Xuding Zhu asked whether there is some k such that all kth power graphs are chromatic-choosable. We answer this question in the negative: we show that there is a positive constant c such that for any k there is a family of graphs G with χ(Gk) unbounded and χl(G) ≥ cχ(Gk) logχ(Gk). We also provide an upper bound, χl(G) < χ(Gk)3 for k > 1. © 2014 Elsevier B.V. All rights reserved. 
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