The generalized coloring numbers $\co_{r}(G)$ (also denoted by $\sco_r(G)$)
and $\wc_r(G)$ of a graph~$G$ are
generalizations of the usual coloring number that have found important
theoretical and algorithmic applications. For each distance~$r$, these
numbers are determined by an ``optimal'' ordering of the vertices
of~$G$. We study the question of whether it is possible to find a single
``uniform'' ordering that is ``good'' for all distances~$r$.
We show that the answer to this question is essentially ``yes''. Our
results give new characterizations of graph classes with bounded
expansion and nowhere dense graph classes.
This is joint work with Jan van den Heuvel.
For Zoom information, please contact Sean at SEngish (at) illinois (dot) edu.
