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Bounded-Degree Independent Sets in Planar Graphs

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Abstract

An independent set of a graph is a set of vertices without edges between them. Every planar graph has an independent set of size at least (1/4)n and there are planar graphs for which any independent set has size at most (1/4)n. In this paper similar bounds are provided for the problem of bounded-degree independent set, i.e., an independent set where additionally all vertices have degree less than a pre-specified bound D. Our upper and lower bounds match (up to a small constant) for D ≥ 16.

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  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Therese Biedl & Dana F. Wilkinson

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  1. Therese Biedl
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  2. Dana F. Wilkinson
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Correspondence to Therese Biedl or Dana F. Wilkinson.

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Biedl, T., Wilkinson, D. Bounded-Degree Independent Sets in Planar Graphs. Theory Comput Syst 38, 253–278 (2005). https://doi.org/10.1007/s00224-005-1139-0

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  • DOI: https://doi.org/10.1007/s00224-005-1139-0

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