Radon numbers grow linearly

Dömötör Pálvölgyi

paper

Radon numbers grow linearly

arXiv:1912.02239

Abstract

Define the $k$ -th Radon number $r_{k}$ of a convexity space as the smallest number (if it exists) for which any set of $r_{k}$ points can be partitioned into $k$ parts whose convex hulls intersect. Combining the recent abstract fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we prove that $r_{k}$ grows linearly, i.e., $r_{k} \leq c (r_{2}) \cdot k$ .

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