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 ${\mathscr C}$ be a hereditary graph class. Say that ${\mathscr C}$ has almost bounded merge-width if, for every fixed $r\in\mathbb{N}$, the radius-$r$ merge-width of its $n$-v…