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Discrete & Computational Geometry
Article . 1998 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
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zbMATH Open
Article
Data sources: zbMATH Open
DBLP
Article . 1998
Data sources: DBLP
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Piercing d -Intervals

Piercing \(d\)-intervals
Authors: Noga Alon;

Piercing d -Intervals

Abstract

This paper contains a very short elementary proof that if \({\mathcal H}\) is a finite family of \(d\)-intervals (a \(d\)-interval is a union of closed intervals in the line) containing no \(k+1\) pairwise disjoint members then the minimum number of points that intersect every member of \({\mathcal H}\) is \(\leq 2d^2k\).

Related Organizations
Keywords

transversal, matching, finite family of \(d\)-intervals, Helly-type theorems and geometric transversal theory, piercing

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    14
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
14
Average
Top 10%
Average
bronze