3 problems

Flip-width subpolynomial collapse conjecture. The following conditions are equivalent:

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…

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…