Comparison of convex hulls and box hulls

Endre Boros, Vladimir Gurvich, Ying Liu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A convex hull of a set of points X is the minimal convex set containing X. A box B is an interval B = {x|x ∈ [a, b], a, b ∈ Rn}. A box hull of a set of points X is defined to be the minimal box containing X. Because both convex hulls and box hulls are closure operations of points, classical results for convex sets can naturally be extended for box hulls. We consider here the extensions of theorems by Carathéodory, Helly and Radon to box hulls and obtain exact results.

Original languageEnglish (US)
Pages (from-to)193-204
Number of pages12
JournalArs Combinatoria
StatePublished - Oct 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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