Sphere-of-Influence Graphs in Normed Spaces

  • Márton Naszódi
  • János Pach
  • Konrad Swanepoel
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 234)


We show that any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than \(5^d k\), thus obtaining a common generalization of results of Füredi and Loeb (Proc Am Math Soc 121(4):1063–1073, 1994 [1]) and Guibas et al. (Sphere-of-influence graphs in higher dimensions, Intuitive geometry [Szeged, 1991], 1994, pp. 131–137 [2]).



We thank the referee for helpful suggestions that improved the paper.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Márton Naszódi
    • 1
  • János Pach
    • 2
  • Konrad Swanepoel
    • 3
  1. 1.Department of GeometryLorand Eötvös UniversityBudapestHungary
  2. 2.EPFL Lausanne and Rényi InstituteBudapestHungary
  3. 3.Department of MathematicsLondon School of Economics and Political ScienceLondonUK

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