Sphere-of-Influence Graphs in Normed Spaces
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 ) and Guibas et al. (Sphere-of-influence graphs in higher dimensions, Intuitive geometry [Szeged, 1991], 1994, pp. 131–137 ).
We thank the referee for helpful suggestions that improved the paper.
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