Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models

We study Koebe orderings of planar graphs: vertex obtained by modelling the graph as intersection pairwise internally-disjoint discs in plane, and ordering vertices non-increasing radii associated discs. prove that for every $d\in \mathbb{N}$, any such has $d$-admissibility bounded $O(d/\ln d)$ weak $d$-coloring number $O(d^4 \ln d)$. This particular shows graphs is d)$, which asymptotically matches a known lower bound due to Dvořák Siebertz.