Kernelization and approximation of distance-r independent sets on nowhere dense graphs

09/15/2018

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by   Michał Pilipczuk, et al.

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For a positive integer r, a distance-r independent set in an undirected graph G is a set I⊆ V(G) of vertices pairwise at distance greater than r, while a distance-r dominating set is a set D⊆ V(G) such that every vertex of the graph is within distance at most r from a vertex from D. We study the duality between the maximum size of a distance-2r independent set and the minimum size of a distance-r dominating set in nowhere dense graph classes, as well as the kernelization complexity of the distance-r independent set problem on these graph classes. Specifically, we prove that the distance-r independent set problem admits an almost linear kernel on every nowhere dense graph class.