5 problems

Ordered matrix removal conjecture. For every $k\times k$ binary matrix $A$ and every $\varepsilon>0$, there is a $\delta=\delta(k,\varepsilon)=\operatorname{poly}(\varepsilon)>0$ s…

Abundance equivalence conjecture. A graph $H$ is $F$-abundant if and only if there is an $F$-colouring $\sigma$ of $H$ such that $(H, \sigma)$ is $F$-abundant.

Arbitrary-group induced removal conjecture. For every $0 < \epsilon < 1/2$, if $A \subseteq G$ is $\epsilon$-far from bi-induced-$F$-free, then

Ordered binary matrix removal lemma. For any finite family $\mathcal{F}$ of ordered binary matrices and any $\epsilon > 0$ there exists $\delta = \delta(\mathcal{F}, \epsilon)$ suc…

Random hypergraph removal conjecture. For every $\delta>0$ and every integer $k\geq 3$, there exist constants $\epsilon>0$ and $C$ such that, if $p\geq Cn^{-1/k}$, then with probab…