5 problems

For every $D\geq 1$ and $\varepsilon>0$, there exists $\delta>0$ such that every $3$-partite $3$-graph $H$ of slicewise VC-dimension at most $D$ that is weakly $\delta$-regular sat…

Viral graph conjecture. For every graph $H$, the family $\{H\}$ is viral.

Bounded-exponent VC-dimension regularity conjecture. For every $\epsilon > 0$, there is a normal subgroup $H$ of $G$ with index at most $\epsilon^{-O_{r,d}(1)}$ and a union $S$ of…

Finite-graph $\mathrm{INT}_f$-minimizing partition conjecture. For every continuous and strictly concave function $f:[0,1]\rightarrow\mathbb R$ and every $\epsilon>0$, there exist…

Let $F_1,F_2,\dots,F_n$ be finite graphs, let $t_1,t_2,\dots,t_m$ be real numbers in $[0,1]$, and let $\mathcal{S}$ be the set of graphons $W$ satisfying … A graphon $W$ has polyno…