Uniform orderings for generalized coloring numbers

Jan van den Heuvel, H. A. Kierstead

Research output: Contribution to journalArticlepeer-review

Abstract

The generalized coloring numbers colr(G) (also denoted by scolr(G)) and wcolr(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and 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.

Original languageEnglish (US)
Article number103214
JournalEuropean Journal of Combinatorics
Volume91
DOIs
StatePublished - Jan 2021

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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