Cliques in dense inhomogenous random graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476966" target="_blank" >RIV/67985840:_____/17:00476966 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/17:00506904
Result on the web
<a href="http://dx.doi.org/10.1002/rsa.20715" target="_blank" >http://dx.doi.org/10.1002/rsa.20715</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 $RG(n,W)$ of the ErdH{o}s--R'{e}nyi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique number of $RG(n,W)$ for each fixed $n$, and give examples of graphons for which $RG(n,W)$ 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
—

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

Project
<a href="/en/project/GA16-07378S" target="_blank" >GA16-07378S: Nonlinear analysis in Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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