A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00508787" target="_blank" >RIV/67985840:_____/19:00508787 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/19:10408156
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1300" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1300</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
Original language description
A large-distance graph is a measurable graph whose vertex set is a measurable subset of R^d, and two vertices are connected by an edge if and only if their distance is larger that 2. We address questions from extremal graph theory in the setting of large-distance graphs, focusing in particular on upper-bounds on the measures of vertices and edges of K_r-free large-distance graphs. Our main result states that if Asubset R^2 is a measurable set such that the large-distance graph on $A$ does not contain any complete subgraph on three vertices then the 2-dimensional Lebesgue measure of A is at most 2pi.
Czech name
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Czech description
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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

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

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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