A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00543158" target="_blank" >RIV/67985840:_____/21:00543158 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/21:10422533
Result on the web
<a href="https://doi.org/10.1007/s00454-020-00183-2" target="_blank" >https://doi.org/10.1007/s00454-020-00183-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-020-00183-2" target="_blank" >10.1007/s00454-020-00183-2</a>
Alternative languages
Result language
angličtina
Original language name
A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
Original language description
Given a measurable set A⊂R^d we consider the 'large-distance graph' G_A, on the ground set A, in which each pair of points from A whose distance is bigger than 2 forms an edge. We consider the problems of maximizing the 2d-dimensional Lebesgue measure of the edge set as well as the d-dimensional Lebesgue measure of the vertex set of a large-distance graph in the d-dimensional Euclidean space that contains no copies of a complete graph on k vertices. The former problem may be seen as a continuous analogue of Turán's classical graph theorem, and the latter as a graph-theoretic analogue of the classical isodiametric problem. Our main result yields an analogue of Mantel's theorem for large-distance graphs. Our approach employs an isodiametric inequality in an annulus, which might be of independent interest.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
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
20
Pages from-to
281-300
UT code for WoS article
000516374700001
EID of the result in the Scopus database
2-s2.0-85107553012