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- W4380876908 abstract "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. Lov'asz and S'os showed that the structure of such graphs is forced by homomorphism densities of graphs with at most $(10q)^q+q$ vertices; subsequently, Lov'asz 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 $qge 2$ 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." @default.
- W4380876908 created "2023-06-17" @default.
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- W4380876908 date "2023-01-01" @default.
- W4380876908 modified "2023-10-04" @default.
- W4380876908 title "Forcing Generalized Quasirandom Graphs Efficiently" @default.
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- W4380876908 doi "https://doi.org/10.5817/cz.muni.eurocomb23-070" @default.
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