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Dvorak (2013) gave a bound on the minimum size of a distance r dominating setin the terms of the maximum size of a distance 2r independent set andgeneralized coloring numbers, thus obtaining a constant factor approximationalgorithm for the parameters in any class of graphs with bounded expansion. Weimprove and clarify this dependence using an LP-based argument inspired by thework of Bansal and Umboh (2017).

On distance r-dominating and 2r-independent sets in sparse graphs