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- W4302336871 abstract "Graphons are analytic objects representing limits of convergent sequences of graphs. Lov'asz and Szegedy conjectured that every finitely forcible graphon, i.e. any graphon determined by finitely many graph densities, has a simple structure. In particular, one of their conjectures would imply that every finitely forcible graphon has a weak $varepsilon$-regular partition with the number of parts bounded by a polynomial in $varepsilon^{-1}$. We construct a finitely forcible graphon $W$ such that the number of parts in any weak $varepsilon$-regular partition of $W$ is at least exponential in $varepsilon^{-2}/2^{5log^*varepsilon^{-2}}$. This bound almost matches the known upper bound for graphs and, in a certain sense, is the best possible for graphons." @default.
- W4302336871 created "2022-10-06" @default.
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- W4302336871 date "2015-06-30" @default.
- W4302336871 modified "2023-09-27" @default.
- W4302336871 title "Weak regularity and finitely forcible graph limits" @default.
- W4302336871 doi "https://doi.org/10.48550/arxiv.1507.00067" @default.
- W4302336871 hasPublicationYear "2015" @default.
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