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Properties of nowhere dense graph classes related to independent set problem

2019/11/27 by Grzegorz Fabiański, Fabiański, Grzegorz
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.1912.00948

Abstract

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.

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