2 problems

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Kwon, McCarty, Oum, and Wollan's rank-depth conjecture for pivot-minor-closed classes
Kwon–McCarty–Oum–Wollan's conjecture. Every pivot-minor-closed class of graphs has bounded rank-depth if and only if it does not contain $P_t$ or $K_t\boxslash K_t$ for some $t$ .
Conjectureopengraph-classes pivot-minors rank-deptharXiv posted 2 days ago
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Minimal-class conjecture for shrub-depth and rank-depth
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…
Conjectureopenhereditary-graph-classes rank-depth shrub-deptharXiv posted 2 days ago

Kwon, McCarty, Oum, and Wollan's rank-depth conjecture for pivot-minor-closed classes