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The choosability of the 2-distance coloring of a graph. (Chinese. English summary) Zbl 1349.05101

Summary: The problem of the choosability of the 2-distance coloring of a graph \(G\) with \(\Delta(G) = 6\) was studied. Using the discharging method to prove that \(\operatorname{ch}_2 (G) \leq 8\) if the maximum average degree \(\operatorname{mad}(G)<2+\frac{16}{25}\), \(\operatorname{ch}_2 (G) \leq 9\) if \(\operatorname{mad}(G)<2+\frac{4}{5}\) for \(\Delta(G) = 6\). The choosability of the list 2-distance coloring of a graph \(G\) with \(\Delta(G) = 6\) is generalized.

MSC:

05C15 Coloring of graphs and hypergraphs
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