Forcing Generalized Quasirandom Graphs Efficiently

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00133884" target="_blank" >RIV/00216224:14330/23:00133884 - isvavai.cz</a>
Result on the web
<a href="https://journals.muni.cz/eurocomb/article/view/35604" target="_blank" >https://journals.muni.cz/eurocomb/article/view/35604</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Forcing Generalized Quasirandom Graphs Efficiently
Original language description
We study generalized quasirandom graphs whose vertex set consists of q parts (of not necessarily the same sizes) with edges within each part and between each pair of parts distributed quasirandomly; such graphs correspond to the stochastic block model studied in statistics and network science. Lovász and Sós showed that the structure of such graphs is forced by homomorphism densities of graphs with at most (10q)^q+q vertices; subsequently, Lovász refined the argument to show that graphs with 4(2q+3)^8 vertices suffice. Our results imply that the structure of generalized quasirandom graphs with q>=2 parts is forced by homomorphism densities of graphs with at most 4q^2-q vertices, and, if vertices in distinct parts have distinct degrees, then 2q+1 vertices suffice. The latter improves the bound of 8q-4 due to Spencer.
Czech name
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Czech description
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Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
European Conference on Combinatorics, Graph Theory and Applications
ISBN
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ISSN
2788-3116
e-ISSN
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Number of pages
8
Pages from-to
503-510
Publisher name
MUNI Press
Place of publication
Brno
Event location
Brno
Event date
Jan 1, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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