Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 1
An Improved Constant Factor for the Unit Distance Problem
Authors:
Péter Ágoston MTA-ELTE Lendület Combinatorial Geometry (CoGe) Research Group, Eötvös Loránd University, Budapest, Hungary
Faculty of Science, Eötvös Loránd University, Budapest, Hungary

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Dömötör Pálvölgyi MTA-ELTE Lendület Combinatorial Geometry (CoGe) Research Group, Eötvös Loránd University, Budapest, Hungary

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Pages:
40–57
Online Publication Date:
01 Apr 2022
Publication Date:
01 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01517
Keywords:
Unit distance graphs; multigraph crossing number; crossing lemma; multigraph crossing lemma
Restricted access

We prove that the number of unit distances among n planar points is at most 1.94 • n4/3, improving on the previous best bound of 8 n4/3. We also give better upper and lower bounds for several small values of n. We also prove some variants of the crossing lemma and improve some constant factors.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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