The r-dynamic chromatic number is bounded in the strong 2-coloring number

A proper vertex-coloring of a graph is r-dynamic if the neighbors of each vertex v receive at least min(r, deg(v)) different colors. In this note, we prove that if G has strong 2-coloring number at most k, then G admits an r-dynamic coloring with no more than (k − 1)r + 1 colors. As a consequence, for every class of graphs of bounded expansion, the r-dynamic chromatic number is bounded by a linear function in r. We give a concrete upper bound for graphs of bounded row-treewidth, which includes for example all planar graphs.