For every graph G, the r-dynamic chromatic number satisfies chi_r(G) <= (scol2(G)-1)r+1, so every bounded-expansion class has chi_r(G) in O(r).
Improved bounds for centered colorings
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The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number
For every graph G, the r-dynamic chromatic number satisfies chi_r(G) <= (scol2(G)-1)r+1, so every bounded-expansion class has chi_r(G) in O(r).