3 problems

Minimal-class conjecture for shrub-depth and rank-depth. Shrub-depth and rank-depth are unbounded in $\mathcal X$ if and only if $\mathcal X$ contains a minimal hereditary class of…

Let $\cf G$ be a class of graphs, let ${\mathrm{CMSO}_1}\xspace$ denote counting monadic second-order logic with one free set-variable type, let $\tau$ be a…

Shrub-depth characterization conjecture. The class $\mathcal{C}$ is of bounded shrub-depth if, and only if, there exists an integer $t$ such that no graph $G\in\mathcal{C}$ contain…