Radon Numbers Grow Linearly

نویسندگان

چکیده

Abstract Define the k -th Radon number $$r_k$$ r k of a convexity space as smallest (if it exists) for which any set points can be partitioned into parts whose convex hulls intersect. Combining recent abstract fractional Helly theorem Holmsen and Lee with earlier methods Bukh, we prove that grows linearly, i.e., $$r_k\le c(r_2)\cdot k$$ ≤ c ( 2 ) · .

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ژورنال

عنوان ژورنال: Discrete and Computational Geometry

سال: 2021

ISSN: ['1432-0444', '0179-5376']

DOI: https://doi.org/10.1007/s00454-021-00331-2