2 problems

Let ${\mathscr C}$ be a hereditary class of graphs. A class is monadically dependent if one cannot interpret all graphs in vertex-colored graphs from the class using a fixed first-…

Let $\mathcal C$ be a hereditary graph class. It has almost bounded merge-width if, for each fixed $r\in\mathbb N$, every $n$-vertex graph in $\mathcal C$ has radius-$r$ merge-widt…