2 problems

Polynomial Rödl dependence conjecture. The dependence of $\delta$ on $d$ can be chosen polynomial; that is, there are constants $C>0$ and $k>0$ such that one may take…

Single-exponential bound conjecture. The correct bound for the size of the largest $\theta$-regular subset guaranteed in every graph is single exponential in $\theta^{-1}$, althoug…