Cliques in dense inhomogenous random graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00506904" target="_blank" >RIV/67985807:_____/17:00506904 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/17:00476966
Result on the web
<a href="http://hdl.handle.net/11104/0298042" target="_blank" >http://hdl.handle.net/11104/0298042</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/rsa.20715" target="_blank" >10.1002/rsa.20715</a>

Result language
angličtina
Original language name
Cliques in dense inhomogenous random graphs
Original language description
The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant urn:x-wiley:10429832:media:rsa20715:rsa20715-math-0001 of the Erdős-Rényi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique number of urn:x-wiley:10429832:media:rsa20715:rsa20715-math-0002 for each fixed n, and give examples of graphons for which urn:x-wiley:10429832:media:rsa20715:rsa20715-math-0003 exhibits wild long-term behavior. Our main result is an asymptotic formula which gives the almost sure clique number of these random graphs. We obtain a similar result for the bipartite version of the problem. We also make an observation that might be of independent interest: Every graphon avoiding a fixed graph is countably-partite.
Czech name
—
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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