Coloring squares of planar graphs with girth six

@article{Dvorak2008ColoringSO,
  title={Coloring squares of planar graphs with girth six},
  author={Zdenek Dvorak and Daniel Kr{\'a}l and Pavel Nejedl{\'y} and Riste Skrekovski},
  journal={Eur. J. Comb.},
  year={2008},
  volume={29},
  pages={838-849}
}
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture is known to be true for g ≥ 7 but false for g ∈ {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth at least six and sufficiently large maximum degree is (∆ + 2)-colorable. 
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