On multiple Borsuk numbers in normed spaces

Zsolt Lángi; Márton Naszódi

doi:10.1556/012.2017.54.1.1352

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 54: Issue 1

On multiple Borsuk numbers in normed spaces

Authors:

Zsolt Lángi

Zsolt Lángi Dept. of Geometry, Budapest University of Technology, Egry József utca 1, Budapest, 1111, Hungary
Morphodynamics Research Group, Hungarian Academy of Sciences, Műegyetem rakpart 1-3., K.261, Budapest, 1111, Hungary

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zlangi@math.bme.hu

and

Márton Naszódi

Márton Naszódi Dept. of Geometry, Eötvös Lóránd University, Budapest, Hungary

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marton.naszodi@math.elte.hu

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Pages:: 13–26

Online Publication Date:: Mar 2017

Publication Date:: 01 Mar 2017

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2017.54.1.1352

Keywords:: Primary 52C17; 05C15; 52A21; Borsuk’s problem; diameter; unique completion; covering; bodies of constant width; complete; multiple chromatic number

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Hujter and Lángi defined the k-fold Borsuk number of a set S in Euclidean n-space of diameter d > 0 as the smallest cardinality of a family F of subsets of S, of diameters strictly less than d, such that every point of S belongs to at least k members of F.

We investigate whether a k-fold Borsuk covering of a set S in a finite dimensional real normed space can be extended to a completion of S. Furthermore, we determine the k-fold Borsuk number of sets in not angled normed planes, and give a partial characterization for sets in angled planes.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Gábor SÁGI (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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