Twin-width and generalized coloring numbers

In Twin-width and generalized coloring numbers paper, we prove that a graph \(G\) with no \(K\, s,s\,\)-subgraph and twin-width \(d\) has \(r\)-admissibility and \(r\)-coloring numbers bounded from above by an exponential function of \(r\) and that we can construct graphs achieving such a dependency in \(r\).

Discrete Mathematics, Volume 345, Issue 3, 2022, 11274