List-coloring the square of a subcubic graph

@article{Cranston2008ListcoloringTS,
  title={List-coloring the square of a subcubic graph},
  author={Daniel W. Cranston and Seog-Jin Kim},
  journal={J. Graph Theory},
  year={2008},
  volume={57},
  pages={65-87}
}
The {\em square} $G^2$ of a graph $G$ is the graph with the same vertex set as $G$ and with two vertices adjacent if their distance in $G$ is at most 2. Thomassen showed that every planar graph $G$ with maximum degree $\Delta(G)=3$ satisfies $\chi(G^2)\leq 7$. Kostochka and Woodall conjectured that for every graph, the list-chromatic number of $G^2$ equals the chromatic number of $G^2$, that is $\chi_l(G^2)=\chi(G^2)$ for all $G$. If true, this conjecture (together with Thomassen's result… 
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