The caratheodory number for the k-core

I. Bárány; M. Perles

doi:10.1007/BF02123009

The caratheodory number for the k-core

I. Bárány^*, M. Perles

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The k-core of the set S ⊂ℝⁿ is the intersection of the convex hull of all sets A ⊆ S with |S{set minus}A|<-k. The Caratheodory number of the k-core is the smallest integer f (d,k) with the property that x ∈ core_{kS, S} ⊂ℝⁿ implies the existence of a subset T ⊆ S such that x ∈ core_kT and |T|≤f (d, k). In this paper various properties of f(d, k) are established.

Original language	English
Pages (from-to)	185-194
Number of pages	10
Journal	Combinatorica
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF02123009
State	Published - Jun 1990

Keywords

AMS subject classification (1980): 52A20

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abstract = "The k-core of the set S ⊂ℝn is the intersection of the convex hull of all sets A ⊆ S with |S{set minus}A|<-k. The Caratheodory number of the k-core is the smallest integer f (d,k) with the property that x ∈ corekS, S ⊂ℝn implies the existence of a subset T ⊆ S such that x ∈ corekT and |T|≤f (d, k). In this paper various properties of f(d, k) are established.",

keywords = "AMS subject classification (1980): 52A20",

author = "I. B{\'a}r{\'a}ny and M. Perles",

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AU - Perles, M.

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N2 - The k-core of the set S ⊂ℝn is the intersection of the convex hull of all sets A ⊆ S with |S{set minus}A|<-k. The Caratheodory number of the k-core is the smallest integer f (d,k) with the property that x ∈ corekS, S ⊂ℝn implies the existence of a subset T ⊆ S such that x ∈ corekT and |T|≤f (d, k). In this paper various properties of f(d, k) are established.

AB - The k-core of the set S ⊂ℝn is the intersection of the convex hull of all sets A ⊆ S with |S{set minus}A|<-k. The Caratheodory number of the k-core is the smallest integer f (d,k) with the property that x ∈ corekS, S ⊂ℝn implies the existence of a subset T ⊆ S such that x ∈ corekT and |T|≤f (d, k). In this paper various properties of f(d, k) are established.

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ER -

The caratheodory number for the k-core

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