Radon Numbers Grow Linearly - Pálvölgyi, Dömötör (Discrete & computational geometry, 2022)
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 ≤ c ( r 2 ) · k .