Properties of nowhere dense graph classes related to independent set problem

11/27/2019

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by   Grzegorz Fabiański, et al.

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A set is called r-independent, if every two vertices of it are in distance greater then r. In the r-independent set problem with parameter k, we ask whether in a given graph G there exists an r-independent set of size k. In this work we present an algorithm for this problem, which applied to a graph from any fixed nowhere dense class, works in time bounded by f(k, r)*G, for some function f. We also present alternative algorithm, with running time bounded by g(k, r)*G, working on slightly more general classes of graphs.