3 problems

Let $\mathcal{B}$ and $\mathcal{F}$ be families consisting respectively of points and pseudo-disks, or of pseudo-disks and points. For a positive integer $m$, let…

Linear-bound conjecture. In fact,

Cover-decomposability conjecture. If $P$ is cover-decomposable, that is, $m_P(2)$ exists, then $P$ is also cover-decomposable into many coverings, so $m_P(k)$ exists.