On the Bi-Lipschitz Geometry of Lamplighter Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355104" target="_blank" >RIV/68407700:21230/21:00355104 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00454-020-00184-1" target="_blank" >https://doi.org/10.1007/s00454-020-00184-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-020-00184-1" target="_blank" >10.1007/s00454-020-00184-1</a>
Alternative languages
Result language
angličtina
Original language name
On the Bi-Lipschitz Geometry of Lamplighter Graphs
Original language description
In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most 6. It follows that lamplighter graphs over countable trees bi-Lipschitzly embed into l1. We study the metric behaviour of the operation of taking the lamplighter graph over the vertex-coalescence of two graphs. Based on this analysis, we provide metric characterisations of superreflexivity in terms of lamplighter graphs over star graphs or rose graphs. Finally, we show that the presence of a clique in a graph implies the presence of a Hamming cube in the lamplighter graph over it. An application is a characterisation, in terms of a sequence of graphs with uniformly bounded degree, of the notion of trivial Bourgain-Milman-Wolfson type for arbitrary metric spaces, similar to Ostrovskii's characterisation previously obtained in Ostrovskii (C. R. Acad. Bulgare Sci. 64(6), 775-784 (2011)).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete & Computational Geometry
ISSN
0179-5376
e-ISSN
1432-0444
Volume of the periodical
66
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
203-235
UT code for WoS article
000517693400001
EID of the result in the Scopus database
2-s2.0-85081350034