4 problems

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…

A graph class has bounded merge-width if, for every fixed radius $r\in\mathbb N$, its radius-$r$ merge-width is bounded by a constant. The paper identifies bounded twin-width and s…

A graph class is hereditary if it is closed under taking induced subgraphs, and it is small if its number of labelled $n$-vertex graphs is at most $n!$. Small-class conjecture. If…

Let $\mathcal C$ be a graph class. Following the paper, say that $\mathcal C$ is in the dense analogue of bounded expansion if, for every weakly sparse graph class $\mathcal D$ suc…