English

Notes about the Caratheodory number

Metric Geometry 2012-12-27 v1 Combinatorics

Abstract

In this paper we give sufficient conditions for a compactum in Rn\mathbb R^n to have Carath\'{e}odory number less than n+1n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory theorem and give a Tverberg type theorem for families of convex compacta.

Cite

@article{arxiv.1112.5942,
  title  = {Notes about the Caratheodory number},
  author = {Imre Barany and Roman Karasev},
  journal= {arXiv preprint arXiv:1112.5942},
  year   = {2012}
}
R2 v1 2026-06-21T19:57:17.840Z