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={Journal of Graph Theory},
  year={2008},
  volume={57},
  pages={65-87}
}
The square G2 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 ∆(G) = 3 satisfies χ(G2) ≤ 7. Kostochka and Woodall conjectured that for every graph, the list-chromatic number of G2 equals the chromatic number of G2, that is χl(G 2) = χ(G2) for all G. If true, this conjecture (together with Thomassen’s result) implies that every planar graph G with ∆(G) = 3… CONTINUE READING

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