On distance ‐dominating and ‐independent sets in sparse graphs
Zdenĕk Dvořák · Journal of Graph Theory · 2018
Abstract Dvořák [European J. Combin. 34 (2013), pp. 833–840] gave a bound on the minimum size of a distance ‐dominating set in terms of the maximum size of a distance ‐independent set and generalized coloring numbers, thus obtaining a constant‐factor approximation algorithm for the parameters in any class of graphs with bounded expansion. We improve and clarify this dependence using a linear programming (LP)‐based argument inspired by the work of Bansal and Umboh [Inform. Process. Lett. 122 (2017), pp. 21–24].