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# 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} }

- Published in Eur. J. Comb. 2008
DOI:10.1016/j.ejc.2007.11.005

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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