Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak regularity and finitely forcible graph limits   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
$\varepsilon^{-2}/2^{5\log^*\varepsilon^{-2}}$. This bound almost matches the
known upper bound for graphs and, in a certain sense, is the best possible for
graphons.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
16
The categories of this paper are: stat