Notes About the Carathéodory Number

By Imre Bárány, Roman N. Karasev. 2011

26 citations recorded by the source corpus.

In this paper we give sufficient conditions for a compactum in ℝn to have Carathéodory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem and give a Tverberg-type theorem for families of convex compacta.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

How researchers see this paper

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In Applied Mathematics

1. Percy Liang
2. Pang Wei Koh
3. Jacob Steinhardt

In Discrete Mathematics and Combinatorics

1. Jacob Steinhardt

In Mathematical Physics

1. Percy Liang
2. Jacob Steinhardt

Citations in the corpus

• Stronger data poisoning attacks break data sanitization defenses (2018, background): “Finding the Carathéodory number of a set is a well-studied problem (see, e.g., Bárány and Karasev (2012), or Mirrokni et al.”