# Induced subdivisions and bounded expansion

## TL;DR

This paper proves that certain graph classes excluding specific induced subgraphs have bounded expansion, providing new characterizations of such classes and strengthening previous results in graph theory.

## Contribution

It establishes that classes of graphs excluding K_s, K_{s,s}, or subdivisions of H as induced subgraphs have bounded expansion, enhancing understanding of graph class properties.

## Key findings

- Graph classes excluding specific induced subgraphs have bounded expansion.
- Provides new characterizations of bounded expansion and nowhere-dense classes.
- Strengthens previous results by Kuhn and Osthus.

## 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 an induced subgraph has bounded expansion; this strengthens a result of Kuhn and Osthus. The argument also gives another characterization of graph classes with bounded expansion and of nowhere-dense graph classes.