Induced subdivisions and bounded expansion

doi:10.1016/j.ejc.2017.10.004

European Journal of Combinatorics

Volume 69, March 2018, Pages 143-148

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Abstract

We prove that for every graph $H$ and for every integer $s$ , the class of graphs that do not contain $K_{s}$ , $K_{s, s}$ , or any subdivision of $H$ as induced subgraphs has bounded expansion; this strengthens a result of Kühn and Osthus (2004). The argument also gives another characterization of graph classes with bounded expansion and of nowhere-dense graph classes.